When a light wave is refracted at a boundary between two different media, it may split into two rays due to optical anisotropy, a phenomenon called birefringence. On the other hand, for a reflected light wave in an ordinary medium, the angle of reflection is always the same as the incident angle as expected from the law of reflection. Here, we report the observation of a split of reflected spin-waves, or bi-reflection of spin-waves, where a spin-wave refers to a wavy motion of electron spins in a magnetic material. We measured the spin-wave propagation in a magnetic garnet Lu2Bi1Fe3.4Ga1.6O12 by using time-resolved magneto-optical microscopy and found that the spin-wave splits in two as a result of reflection at the sample edge of an out-of-plane magnetized film. Systematic measurements combined with calculations unveiled that the bi-reflection is due to the hybridization with elastic waves.