Clustering in a large data set of high dimensionality has always been a serious challenge in the field of data mining. A good clustering method should provide flexible scalability to the number of dimensions as well as the size of a data set. We have proposed a grid-based clustering method called a hybrid-partition method for an on-line data stream. However, as the dimensionality of a data stream is increased, the time and space complexity of this method is increased rapidly. In this paper, a sibling list is proposed to find the clusters of a multi-dimensional data space based on the one-dimensional clusters of each dimension. Although the accuracy of identified multi-dimensional clusters may be less accurate, this one-dimensional approach can provide better scalability to the number of dimensions. This is because the one-dimensional approach requires much less memory usage than the multi-dimensional approach does. Therefore, the confined space of main memory can be more effectively utilized by the one-dimensional approach.