Let (/•") be an increasing sequence of finite rank projections on a separable Hubert space. Assume P" converges strongly to the identity operator /. The quasi triangular operator algebra determined by (Pn) is defined to be the set of ali bounded linear operators T for which lim ||(7-Pn)TPn\\=0. n->oo In this note we prove that two quasitriangular algebras are unitarily equivalent if, and only if, there exists a unital linear isometry mapping one algebra onto the other.