A connector includes a connector housing to be fitted to a counterpart connector housing, a pair of lock arms integrally formed on the connector housing and configured to be engaged with a pair of connecting engagement portions of the counterpart connector housing to lock a state of the connector housings fitted to each other, a pair of wedge pieces configured to be assembled into a wedge insertion hole in the connector housing so as to be movable from a standby position to an unlocking position in the connector housing, the pair of wedge pieces being configured to release, when the pair of wedge pieces are pressed to the unlocking position, a locking of the connector housings fitted to each other. Each of the wedge pieces and the wedge insertion hole has an asymmetrical front and rear cross-sectional shape.