An arrangement configured to connect an evener bar onto a rigid structure of an aircraft engine mount, including a pin system slidingly mounted in a first passageway of a bracket to permit its displacement along a first longitudinal axis, in a first direction from a normal extended position to a retracted position in which the pin system is retracted within this same bracket, and conversely. The arrangement also includes a pin extending member carried by the system and configured to be moved parallel to the longitudinal axis, in a second direction from a normal retracted position to an extended position in which the pin extending member is joined to the system and projects beyond the system, and conversely.