AbstractThis paper focuses on modifying the existing Conjugate Gradient (CG) method of Rivaie, Mustafa, Ismail and Leong (RMIL). The RMIL technique has been the subject of previous studies to enhance its effectiveness. In this study, a new CG search direction, IRMIL, has been presented. This new variation combines the scaled negative gradient, which acts as an initial direction, and a third-term parameter. This paper proves that the IRMIL satisfies the sufficient descent criteria. The method also exhibits global convergence characteristics for exact and strong Wolfe line searches. The methods efficacy is assessed using two distinct methodologies. The first methodology involved conducting numerical tests on conventional Unconstrained Optimisation (UO) problems. The test shows that, while the IRMIL method performs very similarly to other existing CG methods during exact line search, it excels during strong Wolfe line search and converges more quickly. For the second methodology, the NEWMRIL meth.....