An orthonormal wavelet is a function \psi\in L^2(\bold R) such that the system \psi_{jk}(x) = 2^{-j=2}\psi(2^{-j} x - k), k, j\in \bold Z, is an orthonormal basis of L_2(\bold R). The construction of such a \psi from an MRA is rather simple and elegant. There are wavelets that cannot be obtained in this way. Actually, \psi \in L^2(\bold R) is a wavelet if and only if ||\psi||_2\geq 1, \sum_{j\in Z} |\hat\psi(2^j\xi)|^2 = 1 a.e., and, \sum_j\gea0}\hat\psi(2^j\xi)
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\hat\psi(2^j(\xi + 2q\pi)) = 0 a.e., whenever q is an odd integer. These two equations (without the assumption on the norm of) characterize the systems {\psi_{jk}} that are tight frames with constant one. This leads to the question of giving meaning and studying such frames that arise from a construction that extends the one that produced the MRA wavelets. We introduced an appropriate definition, and we can show that our approach is different from and more general than the ones previously obtained by other authors. (This is a joint work with M. Paluszynski, G. Weiss, and S. Xiao.)