In MRI, the flip angle (FA) of slice-selective excitation is not uniform across the slice-thickness dimension. This work investigates the effect of the non-uniform FA profile on the accuracy of a commonly-used method for the measurement, in which the T1 value, i.e., the longitudinal relaxation time, is determined from the steady-state signals of an equally-spaced RF pulse train. By using the numerical solutions of the Bloch equation, it is shown that, because of the non-uniform FA profile, the outcome of the T1 measurement depends significantly on T1 of the specimen and on the FA and the inter-pulse spacing τ of the pulse train. A new method to restore the accuracy of the T1 measurement is described. Different from the existing approaches, the new method also removes the FA profile effect for the measurement of the FA, which is normally a part of the T1 measurement. In addition, the new method does not involve theoretical modeling, approximation, or modification to the underlying principle of the T1 measurement. An imaging experiment is performed, which shows that the new method can remove the FA-, the τ-, and the T1-dependence and produce T1 measurements in excellent agreement with the ones obtained from a gold standard method (the inversion-recovery method).