Metallic glasses have many intrinsic and universal dynamic relaxations observed below the glass-transition temperature. However, these relaxations have mostly been studied on heating and seldom investigated on cooling. In the present work, the slow β and fast β′ relaxations of La60Ni15Al25 metallic glass are studied in sequential heating and cooling experiments under continuous mechanical vibration using a dynamic mechanical analyzer. A slow β relaxation peak is observed on cooling, and compared with the preceding heating step, its peak temperature, activation energy and characteristic relaxation time are all shifted to lower values. On the contrary, a fast β′ relaxation peak is always present on heating, but undetectable on consequent cooling. Only when the metallic glass is cooled below a critical temperature, a certain value of supercooling is achieved, then the fast β′ relaxation is found during subsequent reheating. The work introduces a new approach to investigate dynamic relaxations in metallic glasses and discusses a new possibility of the origin of the fast β’ relaxation.