A method for managing a fuel supply of a spark ignition internal combustion engine (E), the engine (E) being provided with + a fuel supply system (J) suitable for dosing fuel in response to a supply signal, + a three-way catalyst connected to an exhaust manifold of the internal combustion engine having a predetermined oxygen storage capacity, the method comprising a procedure for controlling said combustion so as to alternately oscillate between a lean-burn condition and a rich-burn condition, at least when the catalyst is in a condition of optimal oxygen storage, the method comprising the following steps: - a first step for detecting a cut-off condition, wherein a fuel injection is inhibited, - a second step , upon detection of the cut-off condition, for calculating an excess oxygen stored in said catalyst during the cut-off condition with respect to said optimal oxygen storage, on the basis of a calculation of air ingested by said internal combustion engine (E) during said cut-off condition; - a third step for controlling said fuel supply of the internal combustion engine, at the end of said cut-off condition, so as to neutralize exclusively said excess oxygen with respect to said optimum storage value, wherein said neutralization of said excess oxygen is achieved by increasing the rich-burn time with respect to the lean-burn time during said alternate oscillation between said lean-burn condition and said rich-burn condition or by enriching, during said rich-burn condition, more than leaning during said lean-burn condition. + a fuel supply system (J) suitable for dosing fuel in response to a supply signal, + a three-way catalyst connected to an exhaust manifold of the internal combustion engine having a predetermined oxygen storage capacity, the method comprising a procedure for controlling said combustion so as to alternately oscillate between a lean-burn condition and a rich-burn condition, at least when the catalyst is in a condition of optimal oxygen storage, the method comprising the following steps: - a first step for detecting a cut-off condition, wherein a fuel injection is inhibited, - a second step , upon detection of the cut-off condition, for calculating an excess oxygen stored in said catalyst during the cut-off condition with respect to said optimal oxygen storage, on the basis of a calculation of air ingested by said internal combustion engine (E) during said cut-off condition; - a third step for controlling said fuel supply of the internal combustion engine, at the end of said cut-off condition, so as to neutralize exclusively said excess oxygen with respect to said optimum storage value, - a first step for detecting a cut-off condition, wherein a fuel injection is inhibited, - a second step , upon detection of the cut-off condition, for calculating an excess oxygen stored in said catalyst during the cut-off condition with respect to said optimal oxygen storage, on the basis of a calculation of air ingested by said internal combustion engine (E) during said cut-off condition; - a third step for controlling said fuel supply of the internal combustion engine, at the end of said cut-off condition, so as to neutralize exclusively said excess oxygen with respect to said optimum storage value, wherein said neutralization of said excess oxygen is achieved by increasing the rich-burn time with respect to the lean-burn time during said alternate oscillation between said lean-burn condition and said rich-burn condition or by enriching, during said rich-burn condition, more than leaning during said lean-burn condition. <EOS>