Single-Linkage algorithm is a distance-based Hierarchical clustering method that can find arbitrary shaped clusters but is most unsuitable for large datasets because of its high time complexity. The paper proposes an efficient accelerated technique for the algorithm with a merging threshold. It is a two-stage algorithm with the first one as an incremental pre-clustering step that uses the triangle inequality method to eliminate the unnecessary distance computations. The incremental approach makes it suitable for partial clustering of streaming dataalong with the collection. The second step using the property of the Single-Linkage algorithm itself takes a clustering decision without comparing all the patterns. This method shows how the neighbourhood between the input patterns can be used as a tool to accelerate the algorithm without hampering the cluster quality. Experiments are conducted with various standard and large real datasets and the result confirms its effectiveness for large datasets.