  A degenerate variant of mean field perturbation theory for the on-site
Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms
and perform exact diagonalization in the two-dimensional subspace corresponding
to the degenerate states. The final relations for the second order ground state
energy and first order wave function do not contain singularities at integer
values of the chemical potentials. The resulting equation for the phase
boundary between superfluid and Mott states coincides with the prediction based
on the conventional mean field perturbation approach.
