  A fast algorithm for Antoine and Vandergheynst's (1998) directional
continuous spherical wavelet transform (CSWT) is presented. Computational
requirements are reduced by a factor of O(\sqrt{N}), when N is the number of
pixels on the sphere. The spherical Mexican hat wavelet Gaussianity analysis of
the WMAP 1-year data performed by Vielva et al. (2003) is reproduced and
confirmed using the fast CSWT. The proposed extension to directional analysis
is inherently afforded by the fast CSWT algorithm.
