Law, 20 is enjoying his second loan spell at Valley Parade having spent two months there between October and December 2007, playing ten games in the process - prior to that he had a stint at Yeovil Town.
He returned to City in October 2008 on loan until January, but the Blades have opted to allow the Bantams to extend his stay at Valley Parade until the end of this season where he has made 13 appearances and netted twice to date this season.
Blades boss Kevin Blackwell told the club website: "It is a terrific opportunity for him to play first-team football and further his education."