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 this paper, we propose a new method of defining distances between unrooted binary phylogenetic trees that is especially useful for relatively large phylogenetic trees. Next, we investigate in detail the properties of one example of these metrics, called the Matching Split distance, and describe how the general method can be extended to nonbinary trees.