The development of the shell helium flash or the second helium flash is studied. This phenomenon sets in, after a less massive star has reached the giant branch of a globular cluster, having left the horizontal branch, i.e. after the main helium-burning phase has made a partially degenerate carbon-oxygen core. Temperatures at the helium-burning shell are found to reach higher values than in the first helium flash at the center. This results in a more extended intermediate convection zone in the helium region. Even after the peak of the flash has passed, the helium convection zone is found to extend continually, until its top reaches the bottom of the hydrogen-rich envelope. The mixing of hydrogen into the helium zone may be triggered by the overshoot of convection and/or by the Rayleigh-Taylor instability. Once the mixing has begun, it is accelerated exponentially because of the nuclear energy generation from the mixed hydrogen, until the top of the helium convection zone reaches the bottom of the surface convection zone and large scale mixing lowers the temperature. Carbon and other products of nucleo-synthesis can be transported to the stellar surface. It is suggested that an appreciable fraction of stars may be carbon stars in the very tip of the giant branch of globular clusters.