A well-known preventive replacement policy is the block replacement policy (BRP). In such a policy, items are replaced at constant intervals of time and at failure. The main advantage of this policy lies in its simplicity since the planned replacements occur at regular intervals and so are readily scheduled. The main drawback of the BRP is that it might result in the replacement of a nearly new item at, block replacement time. In this research, a new block replacement policy (NBRP) with used items excluding the wastefulness caused by this drawback is proposed. The objective is to minimize the system's total expected cost per unit time over an infinite time span. This developed model is applicable for general lifetime distribution and the developed NBRP yields a great improvement over other related published policies.