Typical clustering algorithms output a single clustering of the data. However, in real world applications, data can often be interpreted in many different ways; data can have different groupings that are reasonable and interesting from different perspectives. This is especially true for high-dimensional data, where different feature subspaces may reveal different structures of the data. Why commit to one clustering solution while all these alternative clustering views might be interesting to the user. In this paper, we propose a new clustering paradigm for explorative data analysis: find all non-redundant clustering views of the data, where data points of one cluster can belong to different clusters in other views. We present a framework to solve this problem and suggest two approaches within this framework: (1) orthogonal clustering, and (2) clustering in orthogonal subspaces. In essence, both approaches find alternative ways to partition the data by projecting it to a space that is orthogonal to our current solution. The first approach seeks orthogonality in the cluster space, while the second approach seeks orthogonality in the feature space. We test our framework on both synthetic and high-dimensional benchmark data sets, and the results show that indeed our approaches were able to discover varied solutions that are interesting and meaningful. keywords: multi-view clustering, non-redundant clustering, orthogonalization