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