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The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents the historical evolutionary relationship between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In the paper we propose a new method of defining distances between unrooted binary phylogenetic trees that is especially applicable to relatively large phylogenetic trees. Next, we investigate in details properties of one example of these metrics called Matching Split distance.