There was a man named Bjorn who was then on a visit to Thorkell. He was of a somewhat violent character of good family and related in some way to Thorkell. He was not generally liked, because he was too much given to talking against the men who were about Thorkell and drove many away from him. He and Grettir did not get on at all. Bjorn thought him of small account compared to himself; Grettir paid him little deference, and it became an open feud. Bjorn was a boisterous swaggering man, and many of the younger men imitated him, loitering about outside in the evenings.

It happened at the beginning of the winter that a savage brown bear broke out of its den and raged about destroying men and cattle. Every one declared that it had been provoked by the noise which Bjorn and his company made. The beast became most mischievous, attacking the flocks in the very face of the men themselves. Thorkell, being the wealthiest man of that part, suffered most. One day he called up his men to come with him and search out the bear's den. They found it in a cliff by the sea where there was a cave under an overhanging rock, with a narrow path leading to the entrance. Below was a sheer precipice down to the beach, threatening certain death to any one who stumbled. In this den the bear lay in the daytime, going abroad at night. Fences were of no avail against him, nor could the dogs do anything, so that all were in the utmost distress. Thorkell's kinsman Bjorn declared that the main thing was gained now that they had found the den. "Now we shall see," he said, "how the game will go with me and my namesake." Grettir pretended not to hear what he said.

In the evenings when the others retired to bed, Bjorn used generally to go out. One night he went to the bear's den and found the creature inside, growling horribly. He lay down in the path, placing his shield over him, intending to wait until the beast came out as usual. Bruin, however, got wind of him and was rather slow in coming out. Bjorn got very sleepy where he was lying and could not keep awake; in the meantime out came the bear from his den and saw a man lying there. He clawed at him, dragged off his shield and threw it down the cliff. Bjorn woke up, not a little startled, took to his heels and ran off home, narrowly escaping the bear's clutches. His friends knew all about it, having watched his movements; on the next morning they found the shield and made great game of his adventure.

At Yule-time Thorkell himself went out to the den with Bjorn, Grettir and others of his men, a party of eight in all. Grettir had on a fur cape which he put off when they were attacking the bear. It was rather difficult to get at him, since they could only reach him with spear-thrusts, which he parried with his teeth. Bjorn kept urging them on to tackle him, but himself did not go near enough to be in any danger. At last, when no one was looking out, he took Grettir's fur cloak and threw it in to the bear. They did not succeed in getting the bear out, and when night came on turned to go home. Grettir then missed his cloak and saw that the bear had got it into his grip.

"Who has been playing tricks on me?" he cried. "Who threw my cloak into the cave?"

Bjorn answered: "He who did it will not be afraid to say so."

"Things of that sort do not trouble me much," said Grettir.

Then they started on their way home. After they had gone a little way Grettir's garter broke. Thorkell told them to wait for him, but Grettir said it was not necessary. Then Bjorn said: "There is no need to suppose that Grettir will run away from his cloak. He wants to have the honour of killing the beast all alone, and he will say that we eight men went away. Then he would appear to be what he is said to be. He has been backward enough all day."

"I don't know how you stand in that matter," said Thorkell. "You and he are not equal in valour; do not make any to-do about him."

Bjorn said that neither he nor Grettir should choose the words out of his mouth.

There was a hill between them and Grettir, who had turned back along the footpath. Now he had no others to reckon with in making the attack. He drew his sword Jokulsnaut and tied a loop round the handle which he passed over his wrist, because he thought that he could carry out his plans better if his hand were free. He went along the path. When the bear saw a man coming, he charged savagely, and struck at him with the paw that was on the side away from the precipice. Grettir aimed a blow at him with his sword and cut off his paw just above the claws. Then the creature tried to strike him with his sound paw, but to do so he had to drop on the stump, which was shorter than he expected, and over he fell into Grettir's embraces. Grettir seized the beast by the ears and held him off so that he could not bite. He always said that he considered this holding back the bear the greatest feat of strength that he ever performed. The beast struggled violently; the space was very narrow, and they both fell over the precipice. The bear being the heavier came down first on the beach; Grettir fell on the top of him, and the bear was badly mauled on the side that was down. Grettir got his sword, ran it into the heart of the bear and killed him. Then he went home, after fetching his cloak which was torn to pieces. He also took with him the bit of the paw which he had cut off.

Thorkell was sitting and drinking when Grettir entered. They all laughed at the ragged cloak which he was wearing. Then he laid the piece of the paw upon the table. Thorkell said: "Where is my kinsman Bjorn? I never saw iron bite like that in your hands. Now I would like you to show Grettir some honour to make up for the shame which you cast upon him."

Bjorn said that could wait, and that it mattered little to him whether Grettir was pleased or not. Grettir then spoke a verse:

"It is true," said Bjorn, "that you have fought well; and also true that our opinions differ. I suppose you think that your taunts hurt me."

Thorkell said: "I should be glad, Grettir, if you would not revenge yourself upon Bjorn. I will pay the full weregild of a man for you to be reconciled."

Bjorn said he might invest his money better than in paying for that; and that it would be better for him and Grettir to go on bickering since "each oak has that which it scrapes from the other." Thorkell said: "But I ask you, Grettir, to do so much for my sake as not to attack Bjorn while you are both with me."

"That I promise," said Grettir.

Bjorn said that he would walk without fear of Grettir wherever they met. Grettir grinned, and would accept no money on account of Bjorn. They stayed there the winter.