Strong H\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {H}$$\end{document}-tensors play an important role in identifying the positive definiteness of even-order real symmetric tensor. An iterative algorithm for identifying strong H\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {H}$$\end{document}-tensors was given in Li et al. (J Comput Appl Math 255:1–14, 2014), where the method does not stop in finite iterative steps when the tensor is not a strong H\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {H}$$\end{document}-tensor. In this paper, to overcome this drawback, we present a new algorithm which always terminates after finite iterative steps and needs fewer iterations than the earlier one for a general tensor. Numerical examples are given to show the effectiveness of the proposed method.