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Butterfly curves of the subsidiary absorption spin wave instability threshold microwave field amplitude versus static field have been measured at 10 GHz on a 12.8‐μm‐thick single crystal yttrium iron garnet film for two field configurations, one with the static magnetic field in plane and the microwave field out of plane (IP case) and the other with the static field normal to the film plane and the microwave field in plane (PI case). The results for the IP case are similar to earlier results which show a ‘‘kink’’ in the butterfly curve accompanied by a jump of the critical mode wave number k at the kink field. For the PI case, however, there is no observed kink effect. The different butterfly curves for the IP and PI cases are explained on the basis of a new theory for thin films which takes into account the discrete standing wave modes in the film. For the IP case, the theory yields critical modes with wave vectors in the film plane and the kink effect as before. For the PI case, the critical modes have wave vector k components perpendicular to the film plane, the minimum threshold critical modes are modified significantly, and the theory yields smooth butterfly curves with no kink. Quantitative fits to the data were obtained, based on a single trial function for the k‐dependent spin wave linewidth.