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In this work, we theoretically propose and experimentally demonstrate a kind of nonreflecting acoustic metamaterial fence that is perfectly impedance matched to air over a wide range of incident angles and a broad frequency band. The metamaterial fence is composed of an array of rigid cylinders with alternating layers of different cylinder diameters. It is designed by a spatially dispersive effective medium theory and experimentally demonstrated by airborne sound reflectance measurements. Our work provides a unique approach to design and realize rigid acoustic structures that can robustly prohibit reflection and reverberation. Such structures may have important applications in general acoustics.