Suppose Q（ζm） is the m-th cyclotomic number field, where ζm is an m-th primitive root of unity, m1 any integer. Let am=ζm+ζm2+...+ζm（m-1）/2 if m is odd and let βm be the product of the integersl-ζm（1jm, （j, m）=1） if m has at least two distinct prime divisors. It is proved that both am and βm generate power bases of Q（ζm）, i. e., Z [am]= Z[βm]+Z[ζm]. The author also conjectures that there is no other power basis generator except ζm up to equivalence, and proves that this is the case when m=8, 9 and 12. The corresponding result for m=p an odd prime was also obtained by A. Bremner with a different method.
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