The present invention relates to a propulsion unit comprising a pair of contra-rotating coaxial propellers, that are referred to as upstream (2) and downstream (3), the downstream propeller, forming a rotating reference frame, being mounted for rotation about a central member forming a stationary reference frame, and being provided with a device for changing the pitch of the blades, characterized in that the downstream propeller is supported by bearings arranged externally on the cylindrical central support, an upstream bearing (40) of which is arranged downstream of a device for changing the pitch of the blades of the upstream propeller, and in that said device for changing the pitch of the downstream propeller comprises a linear actuator (23) in the stationary reference frame with an element (235) that is able to move axially along the axis of the downstream propeller, the upstream bearing comprising an inner ring that is rigidly connected to the linear actuator and an outer ring that is rigidly connected to a rotating casing (20) of the downstream propeller, and a movement-transmission mechanism (24) connecting said movable element of the linear actuator to the blades, comprising a load-transfer bearing arranged to transmit the axial forces from the linear actuator to the rotating reference frame of the downstream propeller.