  We provide a mathematically proven, simple and efficient algorithm to build
localised Wannier functions, with the only requirement that the system has
vanishing Chern numbers. Our algorithm is able to build localised Wannier for
topological insulators such as the Kane-Mele model. It is based on an explicit
and constructive proof of homotopies for the unitary group. We provide
numerical tests validating the methods for several systems, including the
Kane-Mele model.
