The study of "fixed point theory" comes from the wider area of non-linear functional analysis. A qualitative result which concerns with finding conditions on the structure of the set X and the choice of a mapping f on X, in order to obtain a fixed point, is usually known as a fixed point theorem. In this paper, Kannan type contraction on G-metric space is extended to a pair of self maps, through the flavor of the infimum property of real numbers without an appeal to iterative procedure.