The formation of a pair of dark solitons from a single nonlinear black spin-wave pulse was observed. The experiments were carried out with a long and narrow magnetic yttrium iron garnet film strip in a surface spin-wave configuration. The black spin-wave pulses were excited by the use of microwave black pulses - large-amplitude microwaves with narrow squarelike dips. Pairs of black solitons were observed in certain input power and input black pulse width ranges. For each pair, the two solitons show opposite π phase jumps and an overall phase change of zero. Beyond those power and width ranges, one also observed pairs of gray solitons that showed opposite phase jumps and a zero total phase change. The formation of a single black soliton was also observed, but only for an input black pulse that was very narrow. The experimental observations were reproduced by numerical simulations based on the complex Ginzburg-Landau equation.