  A finite von Neumann algebra $\mathcal{M}$ with a faithful normal trace $%
\tau $ has Haagerup's approximation property (relative to a von Neumann
subalgebra $\mathcal{N}$) if there exists a net $(\phi_{\alpha})_{\alpha\in
\Lambda}$ of normal completely positive ($\mathcal{N}$-bimodular) maps from
$\mathcal{M}$ to $\mathcal{M}$ that satisfy the subtracial condition $% \tau
\circ \phi_{\alpha}\leq \tau $, the extension operators $% T_{\phi_{\alpha}}$
are bounded compact operators (in $<\mathcal{M%},e_{\mathcal{N}}>$), and
pointwise approximate the identity in the trace-norm, i.e.,
$\lim_{\alpha}||\phi_{\alpha}(x)-x||_{2}=0$ for all $% x\in \mathcal{M}$. We
prove that the subtraciality condition can be removed, and provide a
description of Haagerup's approximation property in terms of Connes's theory of
correspondences. We show that if $\mathcal{N}\subseteq \mathcal{M}$ is an
amenable inclusion of finite von Neumann algebras and $% \mathcal{N}$ has
Haagerup's approximation property, then $\mathcal{M}$ also has Haagerup's
approximation property. This work answers two questions of Sorin Popa.
