Nowadays, one-step multi-view clustering algorithms attract many interests. The main issue of multi-view clustering approaches is how to combine the information extracted from the available views. A popular approach is to use view-based graphs and/or a consensus graph to describe the different views. We introduce a novel one-step graph-based multi-view clustering approach in this study. Our suggested method, in contrast to existing graph-based one-step clustering methods, provides two major novelties to the method called Nonnegative Embedding and Spectral Embedding (NESE) proposed in the recent paper [1]. To begin, we use the cluster label correlation to create an additional graph in addition to the graphs associated with the data space. Second, the cluster-label matrix is constrained by adopting some restrictions to make it more consistent. The effectiveness of the proposed method is demonstrated by experimental results on many public datasets.