Sir Pedivere was chasing his wife when Lancelot found them. "Knight, fie for shame, why wilt thou slay this lady?" said Lancelot. "What hast thou to do betwixt me and my wife?" replied Pedivere. "I will slay her maugre thy head." To prevent this, Lancelot rode between them.
Sir Launcelot, said the knight, thou dost not thy part, for this lady hath betrayed me. It is not so, said the lady, truly he saith wrong on me. And for because I love and cherish my cousin germain, he is jealous betwixt him and me; and as I shall answer to God there was never sin betwixt us.
As they were riding and talking, Pedivere called Lancelot's attention to some pretended men of arms riding after them, and lopped off the lady's head when Lancelot's back was turned. He then immediately yielded and would not fight. Lancelot, understandably upset, made him carry the body to Guenevere. She made him take the body to Rome and get his penance from the Pope.
[The] Pope bade him go again unto Queen Guenever, and in Rome was his lady buried by the Pope's commandment. And after this Sir Pedivere fell to great goodness, and was an holy man and a hermit.
T.H. White identifies Pedivere with Bedivere. I find this identification only slightly less improbable than White's combination of Elaine of Carbonek and Elaine of Astolat - it is artistic, but I do not think it is Malory. On the other hand, there is a chance that this Pedivere could be identified with Pedivere of the Straight Marches (below), serving a time at the Grail Castle between his return from Rome and his retirement into a hermitage.
Pedivere of the Straight Marches
Pedyvere of the Strait Marches
When Sir Bors passed the night in the Castle Adventurous (Palace Adventurous) at Carbonek, a spear with a head that seemed to burn like a taper came and wounded him in the shoulder. Then a knight came and bade him arise and fight. Sir Bors "bare him backward until that he came unto a chamber door". The strange knight ducked through the door and rested in that chamber for a long time before coming out to renew the battle. In order to win, Bors had to prevent him from going into the chamber again.
This knight was Pedivere of the Straight Marches. Bors charged him to go to Arthur's court that Whitsunday. The chamber in which Pedivere refreshed himself was very likely that in which the Grail was kept.
This Pedivere might be identified with Pedivere the wife-slayer and hermit.