  The Bergman fan of a matroid is the intersection of tropical hyperplanes
defined by the circuits. A tropical basis is a subset of the circuits set that
defines the Bergman fan. Yu and Yuster posed a question whether every simple
regular matroid has a unique minimal tropical basis of its Bergman fan, and
verified it for graphic, cographic matroids and $R_{10}$. We show every simple
binary matroid has a unique minimal tropical basis. Since the regular matroid
is binary, we positively answered the question.
