For any two polynomials on two variables with a nonzero constant Jacobian determinant, there corresponds a polynomial map known as a Keller map. Assume $\sigma$ is a Keller map which is not injective. In this talk, we obtain a property of $\sigma$ at infinity. This is the first of three main results in the speaker's paper entitled ``a proof of 2-dimensional Jacobian conjecture'' at arXiv:1603.01867.