We　propose　a　simple　and　novel　scheme　to　generate　a　NOON　state　for　the　atoms　trapped　in　two　separate　cavities　by　means　of　single-photon　detection.　The　light–atom　interaction　entangles　the　frequency　spectrum　of　light　and　the　atomic　collective　spins,　and　the　photon–atom　entangled　state　is　converted　to　a　purely　atomic　NOON　state　by　time-resolved　detection　on　the　transmitted　photon.　The　fidelity　of　the　NOON　state　reduces　in　the　presence　of　dissipation.　We　further　propose　an　effective　protocol　to　improve　the　fidelity,　which　yields　a　high-fidelity　many-atom　NOON　state.　Our　scheme　can　be　implemented　with　the　current　technology.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.