Wavelets on the sets of M-positive vectors are studied. Such a set,
associated with a matrix M, is a multidimensional analog of the half-line in Walsh analysis (associated with a number M). Following the ideas of Walsh analysis, the space of M-positive vectors is equipped with a coordinate-wise addition. It is known that harmonic analysis on this space is similar to the Walsh harmonic analysis, in particular, the Fourier transform is such that there exists a class of so-called test functions (with a compact support of the function itself and of its Fourier transform). Wavelet frames consisting of the test functions are of special interest because they may be useful for applications to signal processing, that was confirmed already by using some examples on the half-line. A method for constructing dual wavelet frames is developed in the paper.