  We evaluate the Berry phase for a "missing" family of the square integrable
wavefunctions for the linear harmonic oscillator, which cannot be derived by
the separation of variables (in a natural way). Instead, it is obtained by the
action of the maximal kinematical invariance group on the standard solutions. A
simple closed formula for the phase (in terms of elementary functions) is found
by integration with the help of a computer algebra system.
