PURPOSE: A coolant pump assembly is provided to connect the shaft of motor and the shaft of coolant pump with a flexible coupling unit, which has a gear, in order to attenuate the axial vibration. CONSTITUTION: A second tooth-shape member (102) of an upper shaft (301) assembly is lead-in to a second engaging unit (203) of the coupling unit housing. A first tooth-shape member (302) of the upper shaft assembly is lead-in to a first engaging unit (201) of the coupling unit housing. The rotary shaft is arranged by engaging the second tooth-shape member and the second engaging unit, and by engaging the first tooth-shape member and the first engaging unit. The shaft arrangement is adjusted by rotating a vibration shaft (101) and the upper shaft even if the arrangement of one shaft is bad.