Search for experimental designs which aid in research studies involving large number of treatments with minimal experimental units has been desired overtime. This paper constructs some new series of three associate Partially Balanced Incomplete Block (PBIB) designs having n(n 2)/ 4 treatments with three associate classes in two replicates using the concept of triangular association scheme. The design is constructed from an even squared array of n rows and n columns (n 8) with its both diagonal entries bearing no treatment entries and that given the location of any treatment in the squared array, the other location of the same treatment in the array is predetermined. The design and association parameters fora general case of an even integer n 8 are obtained with an illustrated case for n = 8. Efficiencies of the designs within the class of designs are obtained for a general case of even n 8 with a listing of efficiencies of designs with blocks sizes in the interval [8, 22]. The designs constructed have three associate classes and are irreducible to minimum number of associate classes.