A spin current—a flow of spin angular momentum—can be carried either by spin-polarized free electrons or by magnons, the quanta of a moving collective oscillation of localized electron spins, i.e., a spin wave. Traditionally, it was assumed that a spin wave in a magnetic film with spin-sink-free surfaces can transfer energy and angular momentum only along its propagation direction. In this work, using Brillouin light-scattering spectroscopy in combination with a theory of dipole-exchange spin-wave spectra, we show that in obliquely magnetized free magnetic films, the in-plane propagation of spin waves is accompanied by a transverse spin current along the film normal without any corresponding transverse transport of energy. This work has been published in Physical Review Research and can be accessed here.