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We construct a Brownian path conditioned on its minimum value over a fixed time interval by simple transformations of a Brownian bridge. Path transformations have proved useful in the study of Brownian motion and related processes, by providing simple constructions of various conditioned processes such as Brownian bridge, meander and excursion, starting from an unconditioned Brownian motion. As well as providing insight into the structure of these conditioned processes, path constructionsdoi:10.1214/ecp.v4-1003 fatcat:rw6hs6fw7vghzdael4rhfj7v6m