  We revisit the issue of continuous signature transition from Euclidean to
Lorentzian metrics in a cosmological model described by FRW metric minimally
coupled with a self interacting massive scalar field. Then, using a
noncommutative phase space of dynamical variables deformed by Generalized
Uncertainty Principle (GUP) we show that the signature transition occurs even
for a model described by FRW metric minimally coupled with a free massless
scalar field accompanied by a cosmological constant. This indicates that the
continuous signature transition might have been easily occurred at early
universe just by a free massless scalar field, a cosmological constant and a
noncommutative phase space deformed by GUP, without resorting to a massive
scalar field having an {\it ad hoc} complicate potential. We also study the
quantum cosmology of the model and obtain a solution of Wheeler-DeWitt equation
which shows a good correspondence with the classical path.
