Measurement error is an important factor in evaluating the reliability of a measurement method. In a previous paper, we proposed a new method that measures the permittivity and permeability of materials: a cylindrical material is placed perpendicular to the narrow walls inside a rectangular waveguide, and its constitutive parameters are extracted from the measurement of S-parameters. The new method improved the accuracy of the permeability at the cost of reducing the accuracy of the permittivity. In this letter, we show that by shifting the cylinder from the centre of the waveguide toward the broad wall, the accuracy of the permittivity will increase. An error sensitivity study and the measurement of POM material in the S-band are performed to support our claim.