  In this article, we define a doubling procedure for the bialgebra of
specified Feynman graphs introduced in a previous paper \cite {DMB}. This is
the vector space generated by the pairs $(\bar \Gamma, \bar \gamma)$ where
$\bar \Gamma$ is a locally $1PI$ specified graph of a perturbation theory $\Cal
T$ with $\bar \gamma \subset \bar \Gamma$ locally $1PI$ and where $\bar \Gamma
/ \bar \gamma $ is a specified graph of $\Cal T$. We also define a convolution
product on the characters of this new bialgebra with values in an endomorphism
algebra, equipped with a commutative product compatible with the composition.
We then express in this framework the renormalization as formulated by A.
Smirnov \cite [\S 8.5, 8.6] {Sm}, adapting the approach of A. Connes and D.
Kreimer for two renormalization schemes: the minimal renormalization scheme and
the Taylor expansion scheme. Finally, we determine the finite parts of Feynman
integrals using the BPHZ algorithm after dimensional regularization procedure,
by following the approach by P. Etingof \cite{PE} (see also \cite{RM}).
