A fluid-powered linear motor with rotary pistons is disclosed. An application is for a downhole motor but it could be used in other applications. Rotational pistons provide increased torque generation as the torque generated is proportional to motor length. Since downhole drills are long (generally up to a maximum length of 30 ft.), a high-torque motor can be produced using this method. A pressurized fluid is used to drive the piston assemblies to produce bit shaft power. This concept employs rotary pistons and a mechanical rectifier to convert the rotational reciprocation produced by a reciprocating rotational piston into continuous rotary motion. Integration of synthetic diamond bearing assemblies into the motor allows for reduced friction and abrasive drilling fluid compatibility.