  A successive gauge transformation operator $T_{n+k}$ for the discrete KP(dKP)
hierarchy is defined, which is involved with two types of gauge transformations
operators. The determinant representation of the $T_{n+k}$ is established,and
then it is used to get a new $tau$ function $\tau^{(n+k)}_\triangle$ of the dKP
hierarchy from an initial $\tau_\triangle$. In this process, we introduce a
generalized discrete Wronskian determinant and some useful properties of
discrete difference operator.
