Reversible quiver for performing the sport of archery, consisting of a support element (1) equipped with devices to secure it to the body of the sportsperson, and a containment element (2) for the arrows, which can be connected in an interchangeable fashion to the support element (1), wherein the connection devices (3) are of magnetic type, consisting of a female part (3a) and a male part (3b), and wherein this latter part can be inserted coaxially into the female part (3a), whilst disengagement occurs in the direction defined by the respective disengagement grooves provided on the female parts (3) and equipped with a single disengagement opening.