Symplectic groupoid of unipotent triangular forms was introduced by A.Bondal who studied the induced Poisson bracket on the space of the unipotent upper triangular matrices. We discuss the collection of so-called log-canonical coordinates on the upper-triangular matrices compatible with the Poisson bracket that gives a cluster structure on the symplectic groupoid.

As a byproduct we obtain cluster coordinates on the Teichmueller space of genus 2 closed hyperbolic surfaces which is a new result to the best of our knowledge.

This is a joint work with L. Chekhov.