Starting from any two given multiresolution analyses of $ L _{ 2 } $ , $ {V ^{ 1 } _{ j } } _{ j \in Z } $ , and $ {V ^{ 2 } _{ j } } _{ j \in Z } $ , we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (CDF), which starts from a well-chosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.