A hand-held endless belt abrading machine comprises a base portion and a main portion, which portion is rotatable relative to the base portion around an axis extending in a forward and rearward direction of the abrading machine. The main portion comprises an air motor having a rotational shaft extending in a direction transverse to the abrading machine and projecting from the left end of the air motor, so that an abrading endless belt assembly drivingly connected to the output shaft is positioned to the left relative to the motor and the base portion which is held by a hand of an operator. When a left-handed person uses the abrading machine, the main portion is turned 180° relative to the base portion to shift the abrading endless belt assembly to the right relative to the base portion, thereby enabling the operator to readily observe the abrading belt assembly in operation.