In 2006, existence and uniqueness of coupled fixed point was discussed by Bhaskar and Lakshmikantham [2]. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [1]. In [7], quartet fixed point was introduced and some other related results were obtained in a partially ordered complete metric space. In this paper, a new type of quartet fixed point is introduced and existence and uniqueness of quartet fixed points is considered in a partially ordered complete metric space.