  The states $|\alpha,m>$, defined as ${a^{\dagger}}^{m}|\alpha>$ up to a
normalization constant and $m$ is a nonnegative integer, are shown to be the
eigenstates of $f(\hat{n},m)\hat{a}$ where $f(\hat{n},m)$ is a nonlinear
function of the number operator $\hat{n}$. The explicit form of $f(\hat{n},m)$
is constructed. The eigenstates of this operator for negative values of $m$ are
introduced. The properties of these states are discussed and compared with
those of the state $|\alpha,m >$.
