An air and fuel injection system for the back of a turbomachine's annular combustion chamber, including a central injector and a peripheral annular fuel injector including at least one fuel injection aperture made in an annular wall and emerging in a peripheral annular channel separated from a central channel by the annular wall and having an annular space of admission of air. The system also includes multiple air ejection apertures made in the annular wall downstream from the fuel ejection aperture or apertures in reference to the flow of the air stream, for an additional injection of air into the channel.