Wavelets on the spaces of M-positive vectors are studied. Such a space is a multidimensional analog of the half-line in Walsh analysis. Similarly to the half-line, in this spaces there exists a class of compactly supported test functions having compactly supported Fourier transforms. Wavelet frames consisting of the test functions are of special interest because they may be useful for applications to signal processing. The paper suggests a method of constructing dual wavelet frames of such a type. Bibliography: 12 titles.