Geometric constants play an important role in the research of the geometry of Banach spaces. The definition of the new constant R_1（ X） is given. It is proved that the Banach spaces X with R_1（ X） 2 has the weak fixed point property. The specific values in c_0 space and Orlicz sequence space equipped with Luxemburg norm are calculated. By comparing the values of R_1（ lp） with R（ lp）

R_1（ X） and R（ X） are two different geometric constants.