Note on "Vacuum stability of a general scalar potential of a few fields"

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 $\mathbf{H}$.