  The purpose of this letter is to point out that some conclusions in the paper
(Eur. Phys. J. C {\bf 76}, 324(2016)) are incomplete, and to give complete and
improved conclusions. The analytic necessary and sufficient conditions are
given for the boundedness-from-below conditions of general scalar potentials of
two real scalar fields $\phi_1$ and $\phi_2$ and the Higgs bonson $\mathbf{H}$.
