  Let $G$ be a connected reductive group over a $p$-adic field $F$ of
characteristic 0 and let $M$ be an $F$-Levi subgroup of $G.$ Given a discrete
series representation $\sigma$ of $M(F),$ we prove that there exists a locally
constant and compactly supported function on $M(F),$ which generalizes a
pseudo-coefficient of $\sigma.$ This function satisfies similar properties to
the pseudo-coefficient, and its lifting to $G(F)$ is applied to the Plancherel
formula.
