  We consider the (finite) $W$-algebra $W_{m|n}$ attached to the principal
nilpotent orbit in the general linear Lie superalgebra
$\mathfrak{gl}_{m|n}(\mathbb C)$. Our main result gives an explicit description
of $W_{m|n}$ as a certain truncation of a shifted version of the Yangian
$Y(\mathfrak{gl}_{1|1})$. We also show that $W_{m|n}$ admits a triangular
decomposition and construct its irreducible representations.
