The invention relates to a biological wastewater purification method using a reactor including a first compartment (2) and a second compartment (4), the lower parts of which are communicated with one another. The water to be treated enters the first compartment, while the second compartment houses aerobic granular sludge at atmospheric pressure. Oxygen-laden gas is injected into the lower part of the second compartment. The granular sludge forms a bed (5) in the second compartment (4) and the reactor operates in a sequential, discontinuous manner in a cycle comprising two phases, namely: a first anaerobic phase during which the first compartment (2) is vacuum-filled with the water to be treated, after which the pressure is abruptly brought to atmospheric pressure in order to discharge a volume of water rapidly into the second compartment (4); and a second aerobic phase during which gas containing oxygen is injected into the second compartment (4).