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For compactly supported m-band (m≥2, m∈Z) orthonormal multiwavelet systems, an algorithm to construct compactly supported orthogonal multiwavelets from the associated multi-scaling functions is presented in this paper. This method is simple for computation, does not need to solve a set of nonlinear equations in unknown matrices or factorize a polynomial matrix into a special form, and is not restrained by the multiplicity of multiwavelets. It only needs to solve some linear equations and compute some matrices. As an example, the GHM multiwavelets are derived via this method.