  We present a construction of a wavelet-type orthonormal basis for the space
of radial $L^2$-functions in $\R^3$ via the concept of a radial multiresolution
analysis. The elements of the basis are obtained from a single radial wavelet
by usual dilations and generalized translations. Hereby the generalized
translation reveals the group convolution of radial functions in $\R^3$. We
provide a simple way to construct a radial scaling function and a radial
wavelet from an even classical scaling function on $\R$. Furthermore,
decomposition and reconstruction algorithms are formulated.
