The frequency expression for flexural vibrations of the completely free composite piezoelectric polymer plate given in an earlier paper [J. Acoust. Soc. Am. 77, 1939–1945 (1985)] for all modes of the type p/q (p, q=2,3,4,...) is extended to cover all modes of this type for p, q=0,1,2,..., where p and q are the number of nodal lines in the coordinate directions x1 and x2, respectively. Because of the stiffening effect of electrodes deposited on the polymer surface, the expressions for the flexural and twisting rigidities of the composite plate given in the earlier paper for 2n layers are rewritten with the electrodes treated as layers separate from the polymer. Expressions are also given for the rigidities of the composite plate for an odd number of layers, a case not considered in the earlier paper. The frequencies of several modes are computed for a completely free composite piezoelectric polymer plate, a configuration which has application to hydrostatic polymer hydrophones.