Abstract: From the B-spline basis in Ⅰ triangular partition , at first, we got a sufficient and necessary condition under which the function belongs to wavelet space; secondly, by means of this condition, we constructed four non-tensor product compactly supported continuous functions with symmetry; furthermore we demonstrated there are three functions whose shifts form Riesz b asis. Therefore we have obtained bivariate non-tensor product prewavelet with c ompactly support and symmetry in Ⅰ triangular partition.

Key words: bivariate prewavelet, compactly support, non-tensor product