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We study how can an angular momentum coherent state | τ> keeps its form-invariant during time evolution goveed by the Hamiltonian H =f (t)J+ + f* (t)J_ + g (t)Jz.We discuss this topic in the context of boson realization of |τ>.By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials,we derive the wave function (ζlτ>,which tus out to be a single-subscript Hermite polynomial.Based on this result the maintenance of angular momentum coherent state during time evolution is examined,and the value of τ (t) is totally determined by the parameters involved in the Hamiltonian.