Cytokinesis in Schizosaccharomyces pombe begins at mitotic entry, when the site of division is defined by formation of the contractile acto-myosin ring (CAR) at the cell cortex. Contraction of the CAR and formation of the division septum are triggered at the end of mitosis by septation initiation network (SIN) proteins associated with the spindle pole body (SPB). SIN signalling requires activation of the GTPase Spg1p, which is regulated by the bipartite GTPase-activating protein (GAP) Byr4p-Cdc16p. We show that, for Spg1p to associate with the SPB, it must be bound to its GAP or to its mitotic effector, the protein kinase Cdc7p. Analysis of the GAP proteins reveals that the steady-state level of Byr4p reflects that of Spg1p. Furthermore, if the interaction of Byr4p with Spg1p is compromised, the level of Byr4p decreases dramatically. The adaptation of the level of Byr4p to that of Spg1p requires the presence of Cdc16p and is mediated by proteasome-dependent destruction. It requires neither association with the SPB nor an active SIN. We propose a mechanism that limits the amount of the Byr4p-Cdc16p GAP to the amount required to inhibit Spg1p signalling.