Relative cohomology

Question

Let $N$ be a submanifold of $M$, $N \hookrightarrow M$, I consider the exterior forms $\alpha$ on $M$ such that $\alpha_{|N}=0$ and $d\alpha_{|N}=0$ over $N$ and I take the cohomology of the differential $d$, $H^*(M,N, {\bf R})$. Is this cohomology, the relative cohomology of $M$ with respect to $N$?