  The proposal of the possibility of change of signature in quantum cosmology
has led to the study of this phenomenon in classical general relativity theory,
where there has been some controversy about what is and is not possible. We
here present a new analysis of such a change of signature, based on previous
studies of the initial value problem in general relativity. We emphasize that
there are various continuity suppositions one can make at a classical change of
signature, and consider more general assumptions than made up to now. We
confirm that in general such a change can take place even when the second
fundamental form of the surface of change does not vanish.
