Abstract.A new deterministic modelling taking into account the successive emission of prompt neutrons from initial fragments of a fragmentation range {A, Z, TKE} constructed as in the Point-by-Point (PbP) treatment is described. The good agreement of different prompt emission quantities obtained from this modelling (e.g. ν(A), ν(TKE), Eγ(A), Eγ(TKE), etc.) with the experimental data and the results of the PbP model and other Monte-Carlo models validates the present modelling of sequential emission. The distributions of different residual quantities, including the residual temperature distributions P(T) of light and heavy fragments allow to obtain a new parameterisation of P(T) which can be used in the PbP model and the Los Alamos model.