Two sets of identities between unitary minimal Virasoro characters at
levels m = 3, 4, 5 are presented and proven. The first identity sugges
ts a connection between the Ising and the tricritical Ising models sin
ce the m = 3 Virasoro characters are obtained as bilinears of m = 4 Vi
rasoro characters. The second identity gives the tricritical Ising mod
el characters as bilinears in the Ising model characters and the six c
ombinations of m = 5 Virasoro characters which do not appear in the sp
ectrum of the three state Potts model. The implication of these identi
ties on the study of the branching rules of N = 4 superconformal chara
cters into SU(2) x SU(2) characters is discussed.