The analytical relationship that gives the neutron beam flux does not take into account the probability of decay. In this research, we concluded the analytical relationship of the probability non decay of free neutron during the passage of the sample to be analyzed by NAA. And the conclusion of the analytical relationship to the probability of non-capture of the free neutron during the its passage of the sample to be analyzed by NAA in a simpler method than the previous conclusion. We conducted an application study to investigate the effect of the probability non decay of free neutrons, that flowing through sample, On the flux of transient neutron beam, for neutron beam with various large thickness samples and for different energies of neutrons. The effect of probability of neutron decay on neutron beam flux could not be negligible for all the energies which are bigger than of thermal.