Summary: The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in \(S'(\mathbb{R})\). But uniqueness theorem for the present wavelet inversion formula is valid for the space \(S'_F(\mathbb{R})\) obtained by filtering (deleting) (i) all non-zero constant distributions from the space \(S'(\mathbb{R})\), (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution \(\frac{x^2}{1+x^2}=1-\frac{1}{1+x^2}\) we would omit 1 and retain only \(-\frac{1}{1-x^2}\). The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, \((1+kx-2x^2)e^{-x^2})\) is such a wavelet. \(k\) is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.