Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the formψ(x) ＝∑α∈Zs α(α)ψ(Mx-α), x ∈ Rs,sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that limn→∞ M-n ＝ 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.