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We give an example of an orthogonal transformation group of (Sk -1)sphere with codimension-two principal orbits and an action possessing just two isolated singular orbits (cf. [1, p. 214], [4]). This example shows that a theorem of Hsiang and Lawson [2, Theorem 6] should be properly modified. So we give a modified theorem in a correct form. Finally, we give another example due to T. Asoh, which shows that another theorem of Hsiang and Lawson [2, Theorem 5] should be properly modified.

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