  Target mass correction (TMC) is being used to improve the theoretical results
for the nucleon structure functions. This improvement makes the fitting more
reliable with the available experimental data in lepton scattering off the
nucleon . The recent relations, using the Georgi and Politzer approach indicate
that employing TMC effect are cumbersome, long and contains complicated
integrals. Some of these integrals can not be solved exactly and people are
forced to use approximate methods which seems not to give sufficient and
precise results. On the other hand on analysing the TMC effect we encounter
with the threshold problem for nucleon structure which results to have the
structure function in a regions which are physically forbidden. Here we render
a new solution way, based on the re-scaled parton densities to resolve the
difficultly, relating to the TMC effect. Our solution way can be employed
directly and easily to the parton distribution rather than to the nucleon
structure function. There are different options to amend the parton densities.
What we call as third re-scaling is the best one. Using it we are able to
discard the threshold problem for the nucleon structure function without
resorting to apply some auxiliary mathematical tools like the step function
which is plausible by people . On this way we obtain a better agreement for the
nucleon structure function with the available experimental data in comparison
with the ordinary TMC results, based on Georgi and Politzer approach and some
other approaches.
