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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 andimproved conclusions. The analytic necessary and sufficient conditions aregiven for the boundedness-from-below conditions of general scalar potentials oftwo real scalar fields $\phi_1$ and $\phi_2$ and the Higgs bonson $\mathbf{H}$.

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