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The nature of the magnetic state of strong random magnetic anisotropy (RMA) remains elusive. It is unclear whether the RMA and the Ising spin glass systems belong to the same class or not. Here, we demonstrate, by investigations of the static, critical, and slow dynamic properties of a Dy-base bulk metallic glass (BMG), the RMA can be classified to a universal class of glass different from Ising spin glass. The results have implication for understanding the connection between RMA and spin glass and the subtle role of anisotropy in the magnetic transition of disorder and frustrated systems. On the other hand, our study has the significance in developing efficient BMGs for functional applications.