In this paper, we present an improved technique for mean-squared error (MSE) analysis of a normalized gradient algorithm (NGA) for a second-order adaptive infinite impulse response (IIR) notch filter based on an allpass filter. An analytical expression for the MSE is derived by accurately approximating the power spectral density (PSD) of the fluctuation of the steady-state variable coefficient about its mean value. Accuracy of the expression is compared with expressions derived from previous techniques. To verify the analysis, simulations are presented.