Recent deep clustering algorithms take advantage of self-supervised learning and self-training techniques to map the original data into a latent space, where the data embedding and clustering assignment can be jointly optimized. However, as many recent datasets are enormous and noisy, getting a clear boundary between different clusters is challenging with existing methods that mainly focus on contracting similar samples together and overlooking samples near boundary of clusters in the latent space. In this regard, we propose an end-to-end deep clustering algorithm, i.e., Locally Normalized Soft Contrastive Clustering (LNSCC). It takes advantage of similarities among each sample's local neighborhood and globally disconnected samples to leverage positiveness and negativeness of sample pairs in a contrastive way to separate different clusters. Experimental results on various datasets illustrate that our proposed approach achieves outstanding clustering performance over most of the state-of-the-art clustering methods for both image and non-image data even without convolution.