  Inspired by the squared eigenfunction symmetry constraint, we introduce a new
$\ta_k$-flow by ``extending'' a specific $t_n$-flow of discrete KP hierarchy
(DKPH). We construct extended discrete KPH (exDKPH), which consists of
$t_n$-flow, $\ta_k$-flow and $t_n$ evolution of eigenfunction and adjoin
eigenfunctions, and its Lax representation. The exDKPH contains two types of
discrete KP equation with self-consistent sources (DKPESCS). Two reductions of
exDKPH are obtained. The generalized dressing approach for solving the exDKPH
is proposed and the N-soliton solutions of two types of the DKPESCS are
presented.
