Before Henry could pursue his more elevated projects, the assent of the southern Germans, who had not acknowledged the choice of their northern compatriots, had to be gained. Burkhard of Swabia, who had asserted his independence, and who was at that time carrying on a bitter feud with Rudolph, King of Burgundy, whom he had defeated, in 919, in a bloody engagement near Winterthur, was the first against whom he directed the united forces of the empire, in whose name he, at the same time, offered him peace and pardon. Burkhard, seeing himself constrained to yield, took the oath of fealty to the new-elected King at Worms, but continued to act with almost his former unlimited authority in Swabia, and even undertook an expedition into Italy in favor of Rudolph, with whom he had become reconciled. The Italians, enraged at the wantonness with which he mocked them, assassinated him. Henry bestowed the dukedom of Swabia on Hermann, one of his relations, to whom he gave Burkhard's widow in marriage. He also bestowed a portion of the south of Alemannia on King Rudolph in order to win him over, and in return received from him the holy lance with which the side of the Saviour had been pierced as he hung on the cross. Finding it no longer possible to dissolve the dukedoms and great fiefs, Henry, in order to strengthen the unity of the empire, introduced the novel policy of bestowing the dukedoms, as they fell vacant, on his relations and personal adherents, and of allying the rest of the dukes with himself by intermarriage, thus uniting the different powerful houses in the State into one family. Bavaria still remained in an unsettled state. Arnulf the Bad, leagued with the Hungarians, against whom Henry had great designs, had still much in his power, and Henry, resolved at any price to dissolve this dangerous alliance, not only concluded peace with this traitor on that condition, but also married his son Henry to Judith, Arnulf's daughter, in 921. Arnulf deprived the rich churches of great part of their treasures, and was consequently abhorred by the clergy, the chroniclers of those times, who, chiefly on that account, depicted his character in such unfavorable colors.