Pulse width can be conserved when picosecond solitons propagate through a decreasing dispersion fiber of which the group dispersion exponentially decreases along the fiber length at the same rate as the energy loss. However, for keeping local balance of the dispersion and the self phase modulation, the group dispersion of the decreasing dispersion fiber in which sub picosecond solitons propagate should be modified as a result of the combined action of Raman self frequency shift and the third order dispersion. The group dispersion of the decreasing dispersion fiber has been adjusted and the propagation of sub picosecond solitons through a decreasing dispersion fiber has been investigated by solving numerically the generalized nonlinear Schrdinger equation. The results of the numerical simulation are consistent with theory.