There has been rapidly growing interest in the past decade in a new gauge boson which is considerably lighter than the standard model Zboson. A well-known example of this kind is the so-called dark photon, and it is actively searched for in various experiments nowadays. It would be puzzling to have a new gauge boson which is neither massless nor electroweak scale, but possesses a rather small yet nonzero mass. We present a mechanism that can provide a light gauge boson as a result of a mass matrix diagonalization. (C) 2017 The Author(s). Published by Elsevier B. V. This is an open access article under the CC BY license.