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A new way to build wavelet and Gabor’s Parseval frames for L^2(^d) is shown in this paper. In the first case the construction is done using an expansive matrix B, together with only one function hL^2(^d). In the second one, we work with a function gL^2(^d) and two invertible matrixes B and C, with the condition that C^tZ^dZ^d. The only requirement for h and g is that they have to be supported in a set Q, such that the measure of Q is finite and positive. Q has diameter lower than 1, and its border has null measurement. In addition, {B^jQ}_jZ ({T_BjQ}_jZ^d) is a covering of ^d{0} (^d), and {h(B^j)}_jZ ({T_Bjg}_jZ^d) is a Riesz Partition of unity for L^2(^d). Then, it is possible to obtain the Parseval frames with good localization properties, after adding conditions to h (g). At the end, we show two examples of building of wavelet Parseval frames and Gabor’s Parseval frames with a good decay, as required., number=3, journal=Journal of Informatics and Mathematical Sciences, year=2012, month=Dec., pages=325–337