The resistive ballooning mode is studied in a separatrix geometry for parameters consistent with the H-mode. Besides the 'usual' ideal and resistive ballooning modes accessing a second stable regime at large plasma pressure gradients (α), there is another class of resistive ballooning modes, which do not stabilize as a increases. The properties of these modes are discussed in detail. Large pressure gradients associated with the H-mode, near the separatrix, can destabilize this class of rapidly growing resistive ballooning modes. It is found that since these modes are stabilized by increasing plasma pressure, the possibility of a second stable window also exists for these resistive ballooning modes.