We define a new concept of bisymmetry for multibank wavelets. By extending the theory of multiresolution analysis to multibank wavelets, this work also focuses on the study of four-bank compactly supported bisymmetric orthonormal wavelets. Investigations have shown that there is a class of four-bank compactly supported orthonormal wavelets with bisymmetry, in which any wavelet system can be determined uniquely by its low-pass filter. Thus, the least restrictive conditions are needed for forming a wavelet, so that the free degrees can be reserved for application requirements. Also, such wavelet classes can be parameterized. Therefore, the optimal four-bank wavelets with bisymmetry can be found in this class. Some concrete examples with high vanishing moments are also given. These wavelets can avoid prefiltering, process the boundary conveniently, and enjoy the highly efficient computations in application.