Let G/H be a semisimple symmetric space. Generalizing results of Flensted-Jensen we give a sufficient condition for the existence of irreducible closed invariant subspaces of the unitary representations of G induced from unitary finite dimensional representations of H. This provides a method of constructing unitary irreducible representations of G, and we show by examples that for some irreducible admissible representations of G, this method exhibits not previously known unitarity.