  Let $X$ be a real-analytic manifold and $g\colon X\to{\mathbf R}^n$ a proper
triangulable subanalytic map. Given a subanalytic $r$-form $\omega$ on $X$
whose pull-back to every non singular fiber of $g$ is exact, we show tha
$\omega$ has a relative primitive: there is a subanalytic $(r-1)$-form $\Omega$
such that $dg\Lambda (\omega-d\Omega)=0$. The proof uses a subanalytic
triangulation to translate the problem in terms of "relative Whitney forms"
associated to prisms. Using the combinatorics of Whitney forms, we show that
the result ultimately follows from the subanaliticity of solutions of a special
linear partial differential equation. The work was inspired by a question of
Fran\c{c}ois Treves.
