There was living in Thoroddsstad in Hrutafjord a man named Thorbjorn. He was the son of Arnor Downy-Nose, the son of Thorodd who had settled in that side of Hrutafjord which lies opposite to Bakki. Thorbjorn was of all men the strongest, and was called Oxmain. He had a brother named Thorodd, called Drapustuf. Their mother was Gerd, daughter of Bodvar from Bodvarsholar. Thorbjorn was a great swashbuckler and kept a large troop of followers. He was noted for being worse at getting servants than other men, and scarcely paid them any wages. He was not a man easy to deal with. There was a kinsman of his, also named Thorbjorn, called Slowcoach. He was a mariner, and the two namesakes were in partnership together. He was always at Thoroddsstad and people did not think he made Thorbjorn any better. He liked to talk scandal and spoke offensively of several men.

There was a man named Thorir, a son of Thorkell, at Bordeyr. He first lived at Melar in Hrutafjord, and had a daughter named Helga who married Sleitu-Helgi. After the Fagrabrekka affair Thorir went South to Haukadal and lived in Skard, selling the property at Melar to Thorhall the Winelander, the son of Gamli. Thorhall's son Gamli married Rannveig, the daughter of Asmund Longhair, Grettir's sister. They lived at that time in Melar and had a good establishment. Thorir of Skard had two sons, Gunnar and Thorgeir, both promising men, who took over the property from their father, but were always with Thorbjorn Oxmain, and became very overbearing.

In the summer of that year Kormak and Thorgils rode with a kinsman of theirs named Narfi South to Nordrardal on some business. Odd the Needy-Skald had recovered from the hurts which he had received at the horse-fight and was of the party. While they were south of the heath Grettir was journeying from his home at Bjarg with two of Atli's men. They rode to Burfell and then across the neck to Hrutafjord, reaching Melar in the evening, where they spent three nights. Rannveig and Gamli gave Grettir a friendly reception and invited him to stay, but he wanted to return home. Then Grettir learned of Kormak's company having come from the South, and that they were staying at Tunga at night. He prepared to leave Melar at once, and Gamli offered to send some of his men with him. Gamli's brother Grim, who was very smart and active, and another rode with Grettir. The party, five in number, came to Hrutafjardarhals to the west of Burfell, where the great stone called Grettishaf lies; he struggled a long time with that stone, trying to lift it, and delayed his journey thereby until Kormak's party came up. Grettir went towards them and both alighted from their horses. Grettir said it would be more seemly for free men to set to work with all their might instead of fighting with sticks like tramps. Kormak told them to take up the challenge like men and to do their best. So they went for each other. Grettir was in front of his men and told them to see that nobody got behind him. They fought for a time and both were hurt.

On the same day Thorbjorn Oxmain had ridden across the neck to Burfell, and as he returned with Thorbjorn Slowcoach, Gunnar and Thorgeir, the sons of Thorir, and Thorodd Drapustuf, he saw the fight going on. On coming up, Thorbjorn called upon his men to go between them, but they were struggling so furiously that nobody could get at them. Grettir was making a clean sweep of everything round him. Before him were the sons of Thorir. He pushed them back and they both fell over. This made them furious, and the consequence was that Gunnar gave a blow to one of Atli's men which killed him. Thorbjorn on seeing that ordered them to separate, saying that he would give his support to whichever side obeyed him. By then two of Kormak's men had fallen. Grettir saw that it would scarcely do if Thorbjorn joined the opposite side, so he gave up the battle. All those who had fought were wounded. Grettir was much disgusted at their being separated, but both parties rode home and were not reconciled on this occasion.

Thorbjorn Slowcoach made great game of all this, and the relations between the men of Bjarg and Thorbjorn Oxmain became strained in consequence, until at last there was a regular feud, which however broke out later. No compensation was offered to Atli for his man, and he went on as if he knew nothing of it. Grettir stayed at Bjarg till the Tvi-month. It is not known that he and Kormak ever met again; at least it is not mentioned anywhere.