This paper proposes a discrimination index method based on the Jain's fairness index to distinguish researchers with the same H-index. A validity test is used to measure the correlation of D-offset with the parameters, i.e. H-index, the number of cited papers, the total number of citations, the number of indexed papers, and the number of uncited papers. The correlation test is based on the Saphiro-Wilk method and Pearson's product-moment correlation. The result from the discrimination index calculation is a two-digit decimal value called the discrimination-offset (D-offset), with a range of D-offset from 0.00 to 0.99. The result of the correlation value between the D-offset and the number of uncited papers is 0.35, D-offset with the number of indexed papers is 0.24, and the number of cited papers is 0.27. The test provides the result that it is very unlikely that there exists no relationship between the parameters. For this reason, D-offset is proposed as an additional parameter for H-index to differentiate researchers with the same H-index. The H-index for researchers can be written with the format of "H-index: D-offset". D-offset is worthy to be considered as a complement value to add the H-index value. If the D-offset is added in the H-index value, the H-index will have more discrimination power to differentiate the rank of the researchers who have the same H-index.