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In the Spring and Summer of 1075, the Earls of Norfolk and Hereford were conspiring to seize England for themselves, and they enticed Waltheof to join in. He quickly changed his mind, and reconciled with the King, who treated the matter lightly, but at Christmas 1075, Waltheof was brought to trial, his wife (the King's niece) being a witness against him. When the trial resumed in May Waltheof was found guilty and beheaded on St. Giles's Hill (I suppose this is in Winchester, which is where he was tried) on 31 May 1076.
Waltheof and Judith had no sons and two known daughters, (1) Maud, who married first Simon de Saint Liz (Senlis) and second David I King of Scots, and (2) Judith or Alice, who married Ralph de Toni the younger. There may have been a third daughter who married a Robert son of Richard, but this may be a confusion with a daughter of Maud and Simon.
See the second edition of Cokayne's *Complete Peerage*, vol. VI, pp. 638-640. The children are listed in note (f) on page 639.