A detaching method of sheets from a stack of sheets from a stack of sheets and a relative detaching apparatus is disclosed, including at least a gripping head of a handling device of sheets and a nozzle assembly apt to eject an air flow to a lateral edge of a stack of sheets, furthermore including: a storage assembly of pressurised air provided at least with a compressed-air tank equipped with a pressure multiplier and a relative first pressure adjuster; and a high-pressure pipe between the nozzle assembly and the storage assembly intercepted by a fast-opening electrovalve. The nozzle assembly is provided with a nozzle, supplied through the electrovalve, configured as a convergent/divergent spout.