Two sets of identities between unitary minimal Virasoro characters at levels m=3,4,5 are presented and proven. The first identity suggests a connection between the Ising and tricritical Ising models since the m=3 Virasoro characters are obtained as bilinears of m=4 Virasoro characters. The second identity gives the tricritical Ising model characters as bilinears in the Ising model characters and the six combinations of m=5
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Virasoro characters which do not appear in the spectrum of the three state Potts model. The implication of these identities on the study of the branching rules of