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Evaluation and ranking of every author is very crucial as it is widely used to evaluate the performance of the researcher. This article proposes a new method, called Bh-Index, to evaluate the researchers based on the publications and citations. The method is built on h-Index and only the h-core articles are taken into consideration. The method assigns value additions to those articles that receive significantly high citations in comparison to the h-Index of the researcher. It provides a wide range of values for a given h-Index and effective evaluation even for a short period. Use of Bh-Index along with the h-Index gives a powerful tool to evaluate the researchers.