William IV of Burgundy (1088–1157) was count of Mâcon (1102–1157), count of Auxonne (1127–1157), count of Vienne

Count of Vienne

The Count of Vienne was the ruler of the Viennois, with his seat at Vienne, during the period of the Carolingian Empire and after until 1030, when the county of Vienne was granted to the Archdiocese of Vienne....

 (1148–1157) then regent of the county of Burgundy

County of Burgundy

The Free County of Burgundy , was a medieval county , within the traditional province and modern French region Franche-Comté, whose very French name is still reminiscent of the unusual title of its count: Freigraf...

 (1148–1157). He was the son of Stephen I, Count of Burgundy

Stephen I, Count of Burgundy

Stephen I , Count Palatine of Burgundy, sharing his father's nickname "the Rash" , was Count of Burgundy and Count of Mâcon and Vienne....

 and of Béatrice of Louvain. He attempted to abduct his niece Béatrice of Burgundy

Beatrice I, Countess of Burgundy

Beatrice of Burgundy was the only daughter of Renaud III, Count of Burgundy and Agatha of Lorraine. She was the second wife and Empress of Frederick I, Holy Roman Emperor. Her maternal grandparents were Simon I, Duke of Lorraine and his wife Adelaide of Leuven. Beatrice was active at the...

, daughter of Renaud III

Renaud III, Count of Burgundy

Renaud III , son of Stephen I and Beatrix of Lorraine, was the count of Burgundy between 1127 and 1148. Previously, he had been the count of Mâcon since his father's death in 1102, with his brother, William of Vienne....

, but emperor Frederick Barbarossa prevented him and married her in 1156.

William married Poncette (or Alice) de Traves and had the following issue:

1. Stephen II, count of Auxonne who married Judith (d.1173), daughter of Matthias I, Duke of Lorraine
   Matthias I, Duke of Lorraine
   Matthias I was the duke of Lorraine from 1138 to his death as the eldest son and successor of Simon I and Adelaide. Like his forefathers going back to Thierry II and even to Adalbert, he was a stern supporter of the king of Germany and Holy Roman Emperor...
   
    and had issue.
2. Géraud I of Mâcon (1142 - 1184), who married Maurette de Salins, Countess of Vienna (1127-1184) and had issue.