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Fixed priority until Zero Laxity (FPZL) algorithm is the minimally dynamic scheduling algorithm. In FPZL, fixed priorities are assigned to the jobs and are scheduled accordingly until the state of zero laxity is reached and it does not follow any priority order. FPZL concentrates on scheduling more jobs as far as possible. The algorithm which is proposed in this paper is the variant of FPZL which employs the priority order. Instead of giving up processing of some tasks completely, this algorithm completes some portion of the tasks and at the same time if any zero laxity task arrives it takes that task also into consideration and schedules accordingly. In this way, this algorithm tries to process more jobs as compared to the FPZL algorithm and increases the CPU Utilization.