We define Unipn(F2) to be the group of invertible upper-triangular matrices over F2, the field of 2 elements. Letsifori= 1,2,…,n- 1 denote the matrix whosne diagonal entries are all 1, and whose only other nonzero entry is in the ith row and (i+ 1)st column. Then it is easy to see that thesigenerate Unipn(F2). Reiner [4] gave relations among thesi, which he conjectured gave a presentation for Unipn(F2). We show that a subset of these relations suffice to present the group