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, serving a time at the Grail Castle between his return from Rome and his retirement into a hermitage.
Source
Le Morte Darthur | Sir Thomas Malory, 1469-1470