In steady-state evolutionary algorithms, the parent population is updated each time once a new offspring solution is generated. Due to the updation of the parent population, the non-dominated sorting needs to be applied again and again. The repetition of non-dominated sorting makes steady-state algorithms computationally expensive. But the recent study has identified that the insertion of an offspring solution in the known non-domination level structure of solutions does not change the entire structure. So there is no need to apply the complete non-dominated sorting algorithm again and again. In this regard an efficient non-domination level update approach known as ENLU approach was proposed. In steady-state evolutionary algorithm, the same pair of solutions can be compared multiple times in different generations of the algorithm. In this paper, we have performed the same ENLU approach in a different way so that the same pair of solutions is compared only once if they are in the current population. The worst case time complexity of ENLU approach is O(MN2). So for G generations of the steady-state evolutionary algorithm, the worst case time complexity is GO(MN2). In this paper, we have utilized the same ENLU approach which performs the same number of comparisons all the times. The worst case time complexity of our approach is G(O(MN log N) + O(N2)). However, in terms of space complexity the proposed approach requires O(N2) space as compared to O(N) of the ENLU approach. So we have achieved the speedup at the cost of extra space. At the end, we have explored the possibility of parallelism to make the ENLU approach faster.