I will describe how we can use the cluster algebra realization of the standard Lie-Poisson (RBBBBR-type) algebra for SLn obtained in 1998 by Fomin and Zelevinsky to find log-canonical coordinate parameterization for elements of the groupoid of upper-triangular matrices. A brief introduction to the groupoid construction by Weinberg and Mackenzie will be given. Based on a work in progress with Misha Shapiro.