A general one-factor model for short-term interest rates is proposed. Besides the long memory fractionally integrated mean process, the model also consists of a power function of the interest rate as well as the GARCH effect in the conditional variance. The estimation results show that, while there is no evidence for fractional integration in the mean beyond the well-known martingale property, both the power function of the interest rate and the GARCH effect (but not the ARCH effect) are highly significant in the formation of the conditional variance. Test results also confirm a structure change in October 1979 due to the shift in the Federal Reserve monetary policy.