  The paper proves finite model property and decidability for a family of modal
logics. A binary relation $R$ is called pretransitive, if $R^*=\cup_{i\leq m}
R^i$ for some $m\geq 0$, where $R^*$ is the transitive reflexive closure of
$R$. By the height of $(W,R)$ we mean the height of the preorder $(W,R^*)$.
Special partitionings (filtrations) are described for pretransitive frames of
finite height, which implies finite model property and decidability of logics
of these frames.
