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The temperature evolution of the structure of Ni50.0Mn28.7Ga21.3 single crystals exhibiting magnetic shape memory effect was investigated near the martensitic transformation by X-ray diffraction. Upon heating, five-layered modulated monoclinic martensite (10M) with nm, nm, nm, and at room temperature (297 K) changed to an intermediate (10M′) phase with nm, nm, and at a few tenths of kelvin below the transformation to austenite at K. This previously unreported 10M′ phase between 10M martensite and austenite can be described as orthorhombic using axes diagonal to the original a and b axes derived from the cubic L21 cell...