A self-aligning apparatus for a lifting system includes a structure which includes a first element having a first projecting free end and a second projecting free end which each receive at least one sheave at a point of attachment to the first element, and at least two first points of rotation. The at least one sheave cooperates with at least one wire. The at least two first points of rotation are arranged above the at least one sheave's point of attachment to the first element so that the apparatus self-aligns during use in an uneven loading event.