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The present paper is devoted to investigating the two-dimensional realJacobian conjecture. This conjecture claims that if$F=\left(f,g\right):\mathbb{R}^2\rightarrow \mathbb{R}^2$ is a polynomial mapwith $\det DF\left(x,y\right)\ne0$ for all $\left(x,y\right)\in\mathbb{R}^2$,then $F$ is globally injective. With the help of the Newton diagram, we providea new sufficient condition such that the two-dimensional real Jacobianconjecture holds. Moreover, this sufficient condition generalizes the mainresult of [J. Differential Equations {\bf 260} (2016), 5250-5258]. Furthermore,two new classes of polynomial maps satisfying the two-dimensional real Jacobianconjecture are given.

New sufficient condition for the two-dimensional real Jacobian conjecture through the Newton diagram