The author considers non-degenerate hypersurfaces with zero mean curvature of the \((n+ 1)\)-dimensional semi-Euclidean space with index \(s\), \(\mathbb{R}^{n+ 1}_s\). He calls a non-degenerate hypersurface homothetical if it is locally given by graphs of functions \(f(x_1, x_2,\dots, x_n)= f(x_1) f(x_2)\cdots f(x_n)\), where \(f_i\) are functions of one variable. Using the special form of the zero mean curvature differential equation for non-degenerate graphs obtained from this type of functions, he locally classifies all non-degenerate homothetical hypersurfaces with zero mean curvature of \(\mathbb{R}^{n+ 1}_s\).