We characterize the Hunt convolution kernels $\chi$ on ${\mathbf{R}}^n$ ($n\ge 2$) whose the Green type kernels on $D=\left\{\right(x_1,...,x_n)\in {\mathbf{R}}^n$; $x_1\>0\}$, $V_{\chi }:C_{\mathbf{K}}\left(D\right)\ni f$$(\chi *f-\chi *\stackrel{}{}$