Abstract: A near-k-factor of a graph G is a spanning subgraph in which exactly one isolated vertex and all other vertices of order k. In this study, we employ the near-four-factor concept and (m1, m2, …, mr)-cycle system to present a new method for constructing a cyclic 12-fold triple system. Firstly, we would like to propose a new type of cyclic triple system called cyclic triple near factorization, denoted by CTNF(υ). Then, we prove the existence of CTNF(υ) along with an algorithm for starter triples of CTNF(υ) for υ = 12n+2 when, n is even. Finally, we use the construction of CTNF(υ) to demonstrate the existence of [a, b] factorization of 12 Kυ for a a = 8 and b = 4 (υ-1).