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A two-dimensional multi-element phase grating has been designed in terms of the offset refractive index to exhibit the spatially odd symmetry ( antisymmetry ) along one transparent diagonal line with an even number of rectangular elements while leaving other elements in a unit cell opaque. This grating can be engineered to attain a few intriguing phenomena of asymmetric diffraction, including the elimination of equally spaced oblique diffraction lines, the elimination of alternately crossed oblique diffraction lines, and the selection of equally spaced oblique diffraction lines. These phenomena of engineered asymmetric diffraction are well explained via destructive interference between transmitted field amplitudes from paired, dual-paired, and successive elements along the transparent diagonal line.