Non-IID dataset and heterogeneous environment of the local clients are regarded as a major issue in Federated Learning (FL), causing a downturn in the convergence without achieving satisfactory performance. In this paper, we propose a novel Label-wise clustering algorithm that guarantees the trainability among geographically dispersed heterogeneous local clients, by selecting only the local models trained with a dataset that approximates into uniformly distributed class labels, which is likely to obtain faster minimization of the loss and increment the accuracy among the FL network. Through conducting experiments on the suggested six common non-IID scenarios, we empirically show that the vanilla FL aggregation model is incapable of gaining robust convergence generating biased pre-trained local models and drifting the local weights to mislead the trainability in the worst case. Moreover, we quantitatively estimate the expected performance of the local models before training, which offers a global server to select the optimal clients, saving additional computational costs. Ultimately, in order to gain resolution of the non-convergence in such non-IID situations, we design clustering algorithms based on local input class labels, accommodating the diversity and assorting clients that could lead the overall system to attain the swift convergence as global training continues. Our paper shows that proposed Label-wise clustering demonstrates prompt and robust convergence compared to other FL algorithms when local training datasets are non-IID or coexist with IID through multiple experiments.