Extremely narrow 2 ns wide microwave pulses are generated from nonlinear magnetostatic surface waves in yttrium iron garnet films. The shortest output pulse with the highest amplitude is achieved for input power levels of about 300 mW and a carrier frequency below 3.3 GHz. The results are explained within the model based on dipole exchange spin wave modes involved in three magnon processes. The characteristic time for these processes to develop, as estimated from the smallest fall time of output pulse, is 1 ns. The relevant modes are verified by Brillouin light scattering.