  In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach
to continuous wavelet frames on the sphere. The frame is constructed from a
single so-called admissible function by applying the unitary operators
associated to a representation of the Lorentz group, which is square-integrable
modulo the nilpotent factor of the Iwasawa decomposition. We prove necessary
and sufficient conditions for functions on the sphere, which ensure that the
corresponding system is a frame. We strengthen a similar result in \cite{AV99}
by providing a complete and detailed proof.
