We found the 4-order curvature term satisfied the co-variant derivative. Einstein gravity field equation is consist of 2-order curvature terms. Hence, the 4-order curvature term and 2-order curvature terms make new gravity field equation. In this point, Einstein's gravity field equation can be modified by new 4-order curvature term because gravity field equation's term doesn't have to be 2-order term. Indeed, Einstein himself was like that, 0-order term, the cosmological term. Therefore, our theory is based on legitimate facts.