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One of the sources for the improvement in shape memory behavior is the arrest of the irreversible plastic deformation in the process of accumulation of the reversible martensitic deformation. In this regard, so-called high entropy alloys (HEA) [1] attracted our attention due to the non-obvious strengthening mechanism proposed to explain their high strength in terms of the Burgers vector change along the dislocation line because of the existence of its component perpendicular to the gliding plane [2]. HEA might crystallize into ordered structures like B2 [3]. Crystal structure of the austenite for various shape memory intermetallics, including famous NiTi, belongs to this type. Present paper is dedicated to the first observation of the martensitic transformation (MT) and shape memory in TiZrHfCoNiCu HEA family. Roughly, this MT can be described as B2↔B19’ type. It is accompanied by perfect shape memory due to the non-obvious strengthening mechanism mentioned above. Perspectives of this new class of shape memory materials will be discussed.