The paper by Kurkjian and Zelen(1963) introducted the Property A which related to a structural property of concordance matrix of the column incidence matrix. On the other hand, Paik(1985) showed the property of the concordance matrix, which has multinested block circulant pattern matrix, and this structural property was termed Property C by Paik(1985). This paper classifies the incomplete block designs according to the pattern of the concordence matrix which has multi-nested block circulant pattern. The purpose of this classification simplified the solution of reduced normal equation and plan of the design.