A new method for the construction of compactly supported Parseval wavelet frames in L₂(R^d) with any preassigned approximation order n for arbitrary matrix dilation M is proposed. The number of wavelet functions generating a frame constructed in this way is less or equal to (d+1)|detM|−d. The method is algorithmic, and the algorithm is simple to use. The number of generating wavelet functions can be reduced to |detM| for a large class of matrices M.