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In this paper we answer positively a question of whether it is possible for acircle diffeomorphism with breaks to be smoothly conjugate to a rigid rotationin the case when its breaks are lying on pairwise distinct trajectories. Anexample constructed is a piecewise linear circle homeomorphism that has fourbreak points lying on distinct trajectories, and whose invariant measure isabsolutely continuous w.r.t.\ the Lebesgue measure. The irrational rotationnumber for our example can be chosen a Roth number, but not of bounded type.

A circle diffeomorphism with breaks that is smoothly linearizable