  A new method is presented for the construction of a natural continuous
wavelet transform on the sphere. It incorporates the analysis and synthesis
with the same wavelet and the definition of translations and dilations on the
sphere through the spherical harmonic coefficients. We construct a couple of
wavelets as an extension of the flat Mexican Hat Wavelet to the sphere and we
apply them to the detection of sources on the sphere. We remark that no
projections are used with this methodology.
