In two previous Notes published in this journal, a method of measuring probe sheath thickness and ion mass was described using Langmuir probe diagnostics in low pressure xenon plasma close to Maxwellian substance. According to the first Note, this method includes two stages: (i) in a special experiment with known ion mass, the Bohm and Child-Langmuir-Boguslavsky (CLB) equations for cylindrical Langmuir probes used in this xenon plasma were solved jointly to determine the probe sheath thicknesses and Bohm coefficient CBCyl ≈ 1.13; and (ii) in a general experiment, with known CBCyl, the same equations could be solved to obtain the probe sheath thicknesses and the mean ion mass. In the second Note, the (i) stage of this method was refined: the results of the CLB probe sheath model application, which were termed "evaluations," were corrected using the step-front probe sheath model, which was closer to reality in the special experiment with the xenon plasma. This process resulted in a Bohm coefficient of CBCyl ≈ 1.23 for the cylindrical probe. In the present Note, corrected xenon plasma parameters without the influence of the bare probe protective shield were used for the (i) stage of this diagnostic method. This action also refined the Bohm coefficient, lowering it to CBCyl ≈ 0.745 for cylindrical probes. This advance makes the new diagnostics method more objective and reliable.