Binaries that evolved from red giant (RG) binaries through stable Roche lobe overflow follow the mass-orbital period relation if the donor's core is degenerate. This relation is important for the studies of long orbital period blue stragglers, subdwarf B stars, and millisecond pulsars. To examine the influence of mass transfer schemes on this relation, we model the evolution of RG binaries at metallicity Z = 0.02 and Z = 0.001 with two different mass transfer schemes. In one of the scheme, it is assumed that mass transfer only occurs when the donor star's radius is just larger than its Roche lobe radius ('classical' scheme). In another mass transfer scheme, the mass transfer can also occur when the donor's radius is smaller than its Roche lobe radius as proposed by Ritter (1988) and further studied by Kolb & Ritter (1990; 'Kolb' scheme). We find that the mass transfer scheme has a significant influence on the evolution of RG binaries. In these RG binaries initiating mass transfer on the upper part of the RG branch, the final donor masses are smaller and orbital periods are larger in the models with the 'Kolb' scheme, compared with the models with the 'classical' scheme. The difference between orbital periods (donor masses) at the end of mass transfer under two different mass transfer schemes can be up to 500 d (0.04 M-circle dot) for the same donor mass (orbital period). The mass-orbital period relation from these models with the 'Kolb' scheme is above the relation from models with the 'classical' scheme. Additionally, similar to previous studies, we find that the final orbital period at metallicity Z = 0.02 is larger than that at metallicity Z = 0.001 for a given donor mass.