  Let $(X,(p_j))$ be a Fr\'echet space with a Schauder basis and without
continuous norm, where $(p_j)$ is an increasing sequence of seminorms inducing
the topology of $X$. We show that $X$ satisfies the Invariant Subspace Property
if and only if there exists $j_0\ge 1$ such that $\ker p_{j+1}$ is of finite
codimension in $\ker p_{j}$ for every $j\ge j_0$.
