A hybrid vehicle powertrain that has an engine and an electric machine that may separately or jointly provide torque to a multi-speed transmission. A drivetrain including the engine and the motor is controlled to reduce the requested level of torque provided to the transmission during an upshift. The method is initiated by a request for a reduction of the level of torque and checking the operating state of the engine. If the engine is not on, the torque from the motor is reduced. If the engine is on, the torque from the motor is reduced first and then the torque from the engine is reduced to the requested level of torque.