A method in a pneumatic material conveying system, such as a waste conveying system, which conveying system comprises at least one feed point (61) of material, particularly of waste material, a material conveying pipe (100) which is connectable to the feed point (61), a separator device (20) in which the material being conveyed is separated from conveying air, and means (3) for providing a pressure difference in the conveying pipe (100) at least during the conveyance of the material. At least a part of the conveying piping (100) is connectable as a section of a circuit in which conveying air is circulated at least during the conveyance of the material and, in the method, conveying air circulation is connected, at least momentarily, to a reverse direction in relation to the normal conveying direction, at least in a section of the circuit, which section of the circuit is formed by at least a part of the conveying pipe (100), advantageously for removing a possible blockage.