  We introduce and investigate the notion of uniform Lyndon interpolation
property (ULIP) which is a strengthening of both uniform interpolation property
and Lyndon interpolation property. We prove several propositional modal logics
including ${\bf K}$, ${\bf KB}$, ${\bf GL}$ and ${\bf Grz}$ enjoy ULIP. Our
proofs are modifications of Visser's proofs of uniform interpolation property
using layered bisimulations. Also we give a new upper bound on the complexity
of uniform interpolants for ${\bf GL}$ and ${\bf Grz}$.
