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Abstract: Let p be an odd prime and , where m is a positive integer. Let be a qth primitive root of 1 and be the ring of integers in . In [I. Gaál, L. Robertson, Power integral bases in prime-power cyclotomic fields, J. Number Theory 120 (2006) 372–384] I. Gaál and L. Robertson show that if , where is the class number of , then if is a generator of (in other words ) either α is equals to a conjugate of an integer translate of or is an odd integer. In this paper we show that we can remove the hypothesis over . In other words we show that if is a generator of then either α is a conjugate of an integer translate of or is an odd integer. [Copyright &y& Elsevier]