The invention relates to a turbine engine combustion module (10), in particular for an aircraft turbine engine, designed to carry out constant-volume combustion, comprising: at least two combustion chambers (12A, 12B) arranged about an axis, each chamber (12A, 12B, 12C) comprising a compressed gas intake port (16) and a burnt gas exhaust port (18); and an ignition means that triggers combustion in the combustion chambers (12A, 12B, 12C). The module (10) comprises at least one duct (80) which establishes a communication between a first combustion chamber (12A) and at least one second combustion chamber (12B) in order to inject burnt gases from the first combustion chamber (12A) into the second combustion chamber (12B) so as to trigger combustion in the second combustion chamber (12B).