Method for management of a multi-cylinder internal combustion engine the cylinders of which form a first group of at least one cylinder (12a-c) and a second group of at least one cylinder (14a-c), each cylinder (12a-c, 14a-c) having at least one fuel injector (22a-c, 24a-c) and being provided with air through a common air regulator connected to a distributor bringing the air from the regulator to the cylinders (12a-c, 14a-c), the exhaust gases of the first group being evacuated through a first exhaust line provided with a first nitrogen oxide (NOx) trap and those of the second group being evacuated through a second exhaust line, separate from the first, and provided with a second NOx trap, the method being characterised by the fact that it includes the following steps: - supplying the cylinders (12a-c, 14a-c) with air and with fuel in a default fuel-lean combustion mode the air/fuel mixture injected into the cylinders (12a-c) of the first and of the second group having a first and a second air/fuel mass ratio respectively, the two mass ratios (R1, R2) being higher than the stoichiometry ratio, - as soon as one of the NOx traps (38, 40) is saturated with NOx, tripping 54 into a fuel-rich combustion mode, the air/fuel mass ratios (R1, R2) then being lower than the stoichiometric ratio so that an excess of fuel which is only partially burned purges the NOx traps (38, 40) during an oxidation-reduction reaction, and - differentiating the injection of fuel into the groups (12, 14) of cylinders so that the first mass ratio is different from the second mass ratio, and that the NOx trap which was saturated empties more rapidly than the other NOx trap which was only partially full, - returning to the default lean combustion mode when the purge is finished, - to differentiate the fuel injection, at each purge the first mass ratio is adjusted while the second remains constant so that the purges of the NOx traps (38, 40) converge in a few iterations on a complete and substantially simultaneous purge, - when at a purge the first NOx trap is still partially full while the second NOx trap is already entirely purged then, for the following purge, the first air/fuel mass ratio is decreased according to the terms of a geometric series of constant ratio and the second air/fuel mass ratio is unchanged. - supplying the cylinders (12a-c, 14a-c) with air and with fuel in a default fuel-lean combustion mode the air/fuel mixture injected into the cylinders (12a-c) of the first and of the second group having a first and a second air/fuel mass ratio respectively, the two mass ratios (R1, R2) being higher than the stoichiometry ratio, - as soon as one of the NOx traps (38, 40) is saturated with NOx, tripping 54 into a fuel-rich combustion mode, the air/fuel mass ratios (R1, R2) then being lower than the stoichiometric ratio so that an excess of fuel which is only partially burned purges the NOx traps (38, 40) during an oxidation-reduction reaction, and - differentiating the injection of fuel into the groups (12, 14) of cylinders so that the first mass ratio is different from the second mass ratio, and that the NOx trap which was saturated empties more rapidly than the other NOx trap which was only partially full, - returning to the default lean combustion mode when the purge is finished, - to differentiate the fuel injection, at each purge the first mass ratio is adjusted while the second remains constant so that the purges of the NOx traps (38, 40) converge in a few iterations on a complete and substantially simultaneous purge, - when at a purge the first NOx trap is still partially full while the second NOx trap is already entirely purged then, for the following purge, the first air/fuel mass ratio is decreased according to the terms of a geometric series of constant ratio and the second air/fuel mass ratio is unchanged.