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A new type of X-ray diffuse scattering has been found in the early stages of decomposition of the hexagonal phase of Mn-44at.% Al. The diffuse scattering is observed mainly within the basal plane of the reciprocal lattice and differs for the 10l and 11l points. Theoretical calculations of the X-ray diffuse scattering according to the kinematic scattering theory have been performed for the elastically isotropic and anisotropic cases and for precipitates of various forms and orientations with and without a depleted layer surrounding them. In the latter case, a zero-intensity region near the reciprocal-lattice points occurs. There are cases of good agreement between the experimental results and calculations for the precipitates with a depleted layer.