Disclosed is a sleeve for a female contact, its method of manufacture, and also a connector using the sleeve. The sleeve is provided with a first end and a second end presenting, respectively, a rotary symmetry around a common axis, the ends being inter-connected by a plurality of contact blades. Each contact blade presents connecting sections linking the median part of the blade to the first and the second end respectively. The connecting sections describe at least one truncated surface. Applications include the implementation of connectors for high intensity currents, usable especially for electric vehicles.