In　the　two-machine　no-wait　flowshop　scheduling　problem,　a　quick　algorithm　for　makespan　minimization　and　its　complexity　are　presented.　The　properties　of　the　permutation　schedule　in　the　two-machine　no-wait　flowshop　are　analyzed.　It　is　proved　that　the　feasible　solutions　of　the　two-machine　no-wait　flowshop　scheduling　problem　must　exist　in　the　permutation　schedules,　and　the　optimal　solution　of　the　two-machine　no-wait　flowshop　scheduling　problem　can　be　found　in　permutation　schedules.　Finally,　the　complexity　of　the　two-machine　flowshop　scheduling　problem　with　both　regular　jobs　and　no-wait　jobs　is　studied,　and　provide　the　theoretical　base　for　further　exploring　the　two　machine　no-wait　flowshop　scheduling　problem.