  We define a Howe-Moore property relative to a set of subgroups. Namely, a
group $G$ has the Howe-Moore property relative to a set $\mathcal{F}$ of
subgroups if for every unitary representation $\pi$ of $G$, whenever the
restriction of $\pi$ to any element of $\mathcal{F}$ has no non-trivial
invariant vectors, the matrix coefficients vanish at infinity. We prove that a
semisimple group has the Howe-Moore property relatively to the family of its
factors.
