Method for manufacturing a rotor for a synchronous electrical rotating machine, the rotor comprising a hub, made exclusively of a metal or a metal alloy conducting magnetic fields and having a cylindrical outer shape having a predefined radius, and at least a magnetic pole (2, 4), made of permanent magnets realised by the magnetisation of elementary elements (38, 40) made of a magnetisable material, each elementary element having a rectangular parallelepiped form having two main faces (42, 44), two longitudinal faces (46, 48) and two lateral faces (50, 52), characterised in that it comprises: - forming, on the perimeter of the hub, recesses (22, 24), regularly spaced from one another and intended to receive the permanent magnets for forming a magnetic pole, each recess having a width and a length equal to the width and the length of said magnetic pole and provided with a plane bottom surface, and the following successive steps to realise the magnetic pole: - forming a block (37, 74, 76, 78), having a rectangular parallelepiped shape and having two main faces (56, 58), two longitudinal faces (60, 62) and two lateral faces (64, 66), by fixing at least two elementary elements (38,40) one with the other, over their longitudinal faces, with the interposition of an electrical insulator between them, so that the block formed is massive and integral; - machining a main face of the block (37, 74, 76, 78) in order to form a cylindrical face which has a radius which is substantially equal to the radius of the hub; - magnetising the block (37, 74, 76, 78) so that the magnetic axis generated by the magnetisation lies parallel to the longitudinal faces (46, 48) of the elementary elements (38, 40) making the block; and, - fixing the block (37, 74, 76, 78) in the recess of the hub, the other plane main face of the block being fixed on the plane bottom surface of the recess, said block (37, 74, 76, 78) making a portion of the magnetic pole, the steps of forming, machining, magnetising and fixing a block being repeated until the whole magnetic pole (2, 4) has been realised, the blocks (37, 74, 76, 78) being fixed on the hub one next to the other, with the interposition of an electric insulator between blocks. - forming, on the perimeter of the hub, recesses (22, 24), regularly spaced from one another and intended to receive the permanent magnets for forming a magnetic pole, each recess having a width and a length equal to the width and the length of said magnetic pole and provided with a plane bottom surface, and the following successive steps to realise the magnetic pole: - forming a block (37, 74, 76, 78), having a rectangular parallelepiped shape and having two main faces (56, 58), two longitudinal faces (60, 62) and two lateral faces (64, 66), by fixing at least two elementary elements (38,40) one with the other, over their longitudinal faces, with the interposition of an electrical insulator between them, so that the block formed is massive and integral; - machining a main face of the block (37, 74, 76, 78) in order to form a cylindrical face which has a radius which is substantially equal to the radius of the hub; - magnetising the block (37, 74, 76, 78) so that the magnetic axis generated by the magnetisation lies parallel to the longitudinal faces (46, 48) of the elementary elements (38, 40) making the block; and, - fixing the block (37, 74, 76, 78) in the recess of the hub, the other plane main face of the block being fixed on the plane bottom surface of the recess, said block (37, 74, 76, 78) making a portion of the magnetic pole, the steps of forming, machining, magnetising and fixing a block being repeated until the whole magnetic pole (2, 4) has been realised, the blocks (37, 74, 76, 78) being fixed on the hub one next to the other, with the interposition of an electric insulator between blocks. - forming a block (37, 74, 76, 78), having a rectangular parallelepiped shape and having two main faces (56, 58), two longitudinal faces (60, 62) and two lateral faces (64, 66), by fixing at least two elementary elements (38,40) one with the other, over their longitudinal faces, with the interposition of an electrical insulator between them, so that the block formed is massive and integral; - machining a main face of the block (37, 74, 76, 78) in order to form a cylindrical face which has a radius which is substantially equal to the radius of the hub; - magnetising the block (37, 74, 76, 78) so that the magnetic axis generated by the magnetisation lies parallel to the longitudinal faces (46, 48) of the elementary elements (38, 40) making the block; and, - fixing the block (37, 74, 76, 78) in the recess of the hub, the other plane main face of the block being fixed on the plane bottom surface of the recess, said block (37, 74, 76, 78) making a portion of the magnetic pole,