  The next to the leading order Casimir effect for a real scalar field, within
$\phi^4$ theory, confined between two parallel plates is calculated in one
spatial dimension. Here we use the Green's function with the Dirichlet boundary
condition on both walls. In this paper we introduce a systematic perturbation
expansion in which the counterterms automatically turn out to be consistent
with the boundary conditions. This will inevitably lead to nontrivial position
dependence for physical quantities, as a manifestation of the breaking of the
translational invariance. This is in contrast to the usual usage of the
counterterms, in problems with nontrivial boundary conditions, which are either
completely derived from the free cases or at most supplemented with the
addition of counterterms only at the boundaries. We obtain \emph{finite}
results for the massive and massless cases, in sharp contrast to some of the
other reported results. Secondly, and probably less importantly, we use a
supplementary renormalization procedure in addition to the usual regularization
and renormalization programs, which makes the usage of any analytic
continuation techniques unnecessary.
