Content of this paper reflects about class preservation property of cocentroidal matrices. We have identified square matrices of two different classes-1 and 3*, Matrices falling under these classes stand for their unique identity and special algebraic properties. The set of cocentroidal matrices to a given root matrix of any class, either1 or 3, preserves the characteristic property of the corresponding class. Graphical presentation in each case makes the notion more sharper. [* Matrices of class 1 and class 3 are the members of infinite class of square matrices for which the algebraic sum of each column entries ( case of class 1) and sum of each column and each row entries ( case of class 3) remains a real constant; we call this constant – a Libra value.]