A method for controlling an engine unit for a straddled vehicle, the engine unit comprises an engine having a crankshaft and a fuel injector; a rotating electrical machine power-transmittably coupled to the crankshaft, configured to be used in common as a starter motor for rotating the crankshaft and as a generator for generating electric power by a rotating force of the crankshaft, and including a rotor that is configured to rotate together with the rotation of the crankshaft and a stator that faces the rotor, an electromagnetic pickup, having a detection region in a region through which a plurality of detected portions pass, for generating detection signals in accompaniment with passage of the detected portions through the detection region, the plurality of detected portions being arranged on the rotor at intervals in a rotation direction of the rotor; the engine unit further comprises an inverter including a plurality of switching devices (611 to 616) configured to control a current flowing between a battery, which is installed in the straddled vehicle, and the rotating electrical machine, the method comprises executing: a position specifying processing of specifying a position of the crankshaft using the detection signals generated by the electromagnetic pickup, an idle stop control (S17, S18) of stopping combustion by the engine to enter an idle stop state when an idle stop condition is established, a restart control (S41, S42) of performing, when a restart condition is established in the idle stop state, driving of the crankshaft in a forward rotation direction by the rotating electrical machine and actuating of the fuel injector to restart the engine, a swing back control of performing, after the engine is put in the idle stop state and before beginning the drive of the crankshaft in the forward rotation direction, driving of the crankshaft in a reverse rotation direction by the rotating electrical machine to rotate the crankshaft in reverse to a predetermined swing back position, and a start asynchronous injection control (S44 to S47) of making, in the restart control (S41 to S43; S50 to S52), the fuel injector perform asynchronous injection after beginning the drive of the crankshaft in the forward rotation direction by the rotating electrical machine, wherein the method comprises controlling the switching devices (611 to 616) using the detection signals generated by the electromagnetic pickup, and executing, in the start asynchronous injection control (S44 to S47), a forward rotation identification of identifying a beginning of rotation of the crankshaft in the forward rotation direction and making the fuel injector perform the asynchronous injection on condition of the beginning of rotation of the crankshaft in the forward rotation direction being identified by the forward rotation identification, and the forward rotation identification includes a forward synchronous rotation determination of determining, based on the control of the switching devices (611 to 616) and the detection signals generated by the electromagnetic pickup, whether or not timings of the control of the switching devices (611 to 616) and the detection signals are matched. a position specifying processing of specifying a position of the crankshaft using the detection signals generated by the electromagnetic pickup, an idle stop control (S17, S18) of stopping combustion by the engine to enter an idle stop state when an idle stop condition is established, a restart control (S41, S42) of performing, when a restart condition is established in the idle stop state, driving of the crankshaft in a forward rotation direction by the rotating electrical machine and actuating of the fuel injector to restart the engine, a swing back control of performing, after the engine is put in the idle stop state and before beginning the drive of the crankshaft in the forward rotation direction, driving of the crankshaft in a reverse rotation direction by the rotating electrical machine to rotate the crankshaft in reverse to a predetermined swing back position, and a start asynchronous injection control (S44 to S47) of making, in the restart control (S41 to S43; S50 to S52), the fuel injector perform asynchronous injection after beginning the drive of the crankshaft in the forward rotation direction by the rotating electrical machine, wherein the method comprises controlling the switching devices (611 to 616) using the detection signals generated by the electromagnetic pickup, and executing, in the start asynchronous injection control (S44 to S47), a forward rotation identification of identifying a beginning of rotation of the crankshaft in the forward rotation direction and making the fuel injector perform the asynchronous injection on condition of the beginning of rotation of the crankshaft in the forward rotation direction being identified by the forward rotation identification, and the forward rotation identification includes a forward synchronous rotation determination of determining, based on the control of the switching devices (611 to 616) and the detection signals generated by the electromagnetic pickup, whether or not timings of the control of the switching devices (611 to 616) and the detection signals are matched.