  For a stratified pseudomanifold $X$, we have the de Rham Theorem $
\lau{\IH}{*}{\per{p}}{X} = \lau{\IH}{\per{t} - \per{p}}{*}{X}, $ for a
perversity $\per{p}$ verifying $\per{0} \leq \per{p} \leq \per{t}$, where
$\per{t}$ denotes the top perversity. We extend this result to any perversity
$\per{p}$. In the direction cohomology $\mapsto$ homology, we obtain the
isomorphism $$ \lau{\IH}{*}{\per{p}}{X} = \lau{\IH}{\per{t}
-\per{p}}{*}{X,\ib{X}{\per{p}}}, $$ where $ {\displaystyle \ib{X}{\per{p}} =
\bigcup\_{S \preceq S\_{1} \atop \per{p} (S\_{1})< 0}S = \bigcup\_{\per{p} (S)<
0}\bar{S}.} $ In the direction homology $\mapsto$ cohomology, we obtain the
isomorphism $$ \lau{\IH}{\per{p}}{*}{X}=\lau{\IH}{*}{\max (\per{0},\per{t}
-\per{p})}{X}. $$ In our paper stratified pseudomanifolds with
one-codimensional strata are allowed.
