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Photon-magnon coupling, where electromagnetic waves interact with spin waves, and negative refraction, which bends the direction of electromagnetic waves unnaturally, constitute critical foundations and advancements in the realms of optics, spintronics, and quantum information technology. Here, we explore a magnetic-field-controlled, on-off switchable, nonreciprocal negative refraction within a non-Hermitian photon-magnon hybrid system. By integrating an yttrium iron garnet film with an inverted split-ring resonator, we discover pronounced negative refraction driven by the system's non-Hermitian properties. This phenomenon exhibits unique nonreciprocal behavior dependent on the signal's propagation direction. Our analytical model sheds light on the crucial interplay between coherent and dissipative coupling, significantly altering permittivity and permeability's imaginary components, crucial for negative refraction's emergence. This work pioneers new avenues for employing negative refraction in photon-magnon hybrid systems, signaling substantial advancements in quantum hybrid systems., Comment: 27 pages, 4 figures