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It has been recognized that the high damping capacity of MnCu based alloys is closely related to the formation of elastic twins as a result of antiferromagnetic transition and martensitic transformation. However, the mechanism for these transitions in this kind of alloy has not been fully understood. For example, previous investigations ascribed the elastic modulus softening prior to martensitic transformation to antiferromagnetic or pre-martensitic transitions, although no convincing evidence was reported. In this paper, an intensive experimental study was made of the modulus softening and microstructural evolution in a typical high damping Mn-22Cu-5Ni-2Fe alloy, and the evidence of strain glass transition was reported. Such a transition, characterized by a continuous formation of nano-martensite domains, is accompanied by a gradual frequency-dependent modulus softening over a broad temperature range prior to martensitic transformation.