It is believed in particle physics that the velocity-dependent part of potential is, in general, ambiguous as far as it is derived from S-matrix. We consider the most general form of the graviton ·propagator under an arbitrary q-number gauge transformation for the graviton field. The. propagator depends on twelve arbitrary functions of k 2 ,. k being the space part of the momentum . ~f the graviton. The arbitrariness of the gauge functions can be used to remove the ambiguity of orie-gni.viton exchange potential ~p to the order of (G/r) (v/c)4, G being the gravitational constant. The potential thus obtained depends only on one gauge parameter, say x. The perihelion motion of two-body system i:s gauge independent, although the potentials in the order of (G/r) (v/c) 2 and G2/r 2 depend on the gauge parameter x. The potentials are derived from those in a fixed gauge parameter x by a coordinate transformation. Suppose that we are of inter.est to obtain one-particle exchange potential between two elementary particles with masses m1 and m2. Then particle phys icists usually consider the diagram showing' that the p·articles with initial four momenta P1 and P2 and final momenta q1 and q2(P1 2 =q1 2 = -m1 2 ,P 2 2 =q 2 2 = -m 2 2 ) exchange a boson with momentum k= (PI- q1) = - CP2- q 2), and calculate the potential contributed from the S-matrix element corresp.onding to this diagram. However it is well known in particle physics that the v·elocity-dependent part of this potential is ambiguous. Since energy is conserved in any S-matrix element, t~e en.ergy transferred between two particles, ko is equal to (p 10 - q 10) and also to (q20 - p;o): The: ambiguity comes from the ko-dependence of the S-matrix element. To show this explicitly, let us consider one-graviton exchange potential be tween· two' spinless particles. The graviton propagator is proportional to 1