A valve for one-way transfer of air from vacuum storage bags, including a body, a flat diaphragm made of a flexible material, and a holder for securing the diaphragm to the body; a central portion of the body includes an air passage; the diaphragm has a first position where the air passage is covered by a central portion of the diaphragm thus blocking air flow through the air passage, and a second position where the central portion of the diaphragm is reversibly moved away from the air passage thus allowing air flow through the air passage; the diaphragm is secured between the body and the holder, at its three or more distinct edge portions of the diaphragm. A vacuum storage bag equipped with the valve.