  We perform a detailed analysis of renormalization at one-loop order in the
$\lambda\phi^4$ theory with Robin boundary condition (characterized by a
constant $c$) on a single plate at $z=0$. For arbitrary $c\geq0$ the
renormalized theory is finite after the inclusion of the usual mass and
coupling constant counterterms, and two independent surface counterterms. A
surface counterterm renormalizes the parameter $c$. The other one may involve
either an additional wave-function renormalization for fields at the surface,
or an extra quadratic surface counterterm. We show that both choices lead to
consistent subtraction schemes at one-loop order, and that moreover it is
possible to work out a consistent scheme with both counterterms included. In
this case, however, they can not be independent quantities. We study a simple
one-parameter family of solutions where they are assumed to be proportional to
each other, with a constant $\vartheta$. Moreover, we show that the
renormalized Green functions at one-loop order does not depend on $\vartheta$.
This result is interpreted as indicating a possible new renormalization
ambiguity related to the choice of $\vartheta$.
