Disclosed is a motor assembly for a motor unit for driving a shaft for rolling a blind, the assembly including a rotary motor and an output shaft connected to the rotary motor in order to transmit the torque supplied by the rotary motor to the rolling shaft, the output shaft including a first socket for receiving a drive member of the rolling shaft of a roller blind. The output shaft also includes a second socket, separate from the first socket, for securing a non-roller blind to the rolling shaft.