We　propose　a　one-step　scheme　for　driving　many　atoms　into　a　NOON　state.　In　this　scheme,　two　cavities　are　coupled　to　each　other　through　the　photon-hopping　interaction　and　each　cavity　contains　N　four-level　atoms.　The　2N　atoms　are　driven　into　a　NOON　state　via　a　phase-shift　which　depends　on　the　collective　atomic　excitations.　Interestingly,　the　time　of　generating　the　NOON　state　is　independent　of　the　atom　number,　i.e.,　it　is　unchanged　with　the　increasing　of　the　atom　number.　Also,　our　scheme　is　insensitive　to　cavity　decay　and　can　effectively　suppress　atomic　spontaneous　emission.　©　2018　The　Author(s).　Published　by　IOP　Publishing　Ltd　on　behalf　of　Deutsche　Physikalische　Gesellschaft.