We explore a new perspective on adapting the learning rate (LR) schedule to improve the performance of the ReLU-based network as it is iteratively pruned. Our work and contribution consist of four parts: (i) We find that, as the ReLU-based network is iteratively pruned, the distribution of weight gradients tends to become narrower. This leads to the finding that as the network becomes more sparse, a larger value of LR should be used to train the pruned network. (ii) Motivated by this finding, we propose a novel LR schedule, called S-Cyclical (S-Cyc) which adapts the conventional cyclical LR schedule by gradually increasing the LR upper bound (max_lr) in an S-shape as the network is iteratively pruned.We highlight that S-Cyc is a method agnostic LR schedule that applies to many iterative pruning methods. (iii) We evaluate the performance of the proposed S-Cyc and compare it to four LR schedule benchmarks. Our experimental results on three state-of-the-art networks (e.g., VGG-19, ResNet-20, ResNet-50) and two popular datasets (e.g., CIFAR-10, ImageNet-200) demonstrate that S-Cyc consistently outperforms the best performing benchmark with an improvement of 2.1% - 3.4%, without substantial increase in complexity. (iv) We evaluate S-Cyc against an oracle and show that S-Cyc achieves comparable performance to the oracle, which carefully tunes max_lr via grid search.