  We show that a particular set of global modes for the massive de Sitter
scalar field (the de Sitter waves) allows to manage the group representations
and the Fourier transform in the flat (Minkowskian) limit. This is in
opposition to the usual acceptance based on a previous result, suggesting the
appearance of negative energy in the limit process. This method also confirms
that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far
as one wishes to recover ordinary QFT in the flat limit.
