In order to develop a wet razor consisting of a handle, a razor head which can be connected to the front end of the handle, in particular a razor blade unit with at least one razor blade, and a connecting device for connection of the razor head to the handle, to the effect that the results of shaving are improved and the razor can also be used for medical purposes for preoperative shaving, it is proposed that the razor head is mounted so as to be pivotable relative to the handle about a pivot axis located essentially perpendicular to a cutting edge of the razor blade and essentially in the plane of the razor blade.
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