Discovering clusters from a dataset with different shapes, densities, and scales is a known challenging problem in data clustering. In this paper, we propose the RElative COre MErge (RECOME) clustering algorithm. The core of RECOME is a novel density measure, i.e., Relative $K$ nearest Neighbor Kernel Density (RNKD). RECOME identifies core objects with unit RNKD, and {partitions} non-core objects into atom clusters by successively following higher-density neighbor relations toward core objects. Core objects and their corresponding atom clusters are then merged through $α$-reachable paths on a KNN graph. We discover that the number of clusters computed by RECOME is a step function of the $α$ parameter with jump discontinuity on a small collection of values. A fast jump discontinuity discovery (FJDD) method is proposed based on graph theory. RECOME is evaluated on both synthetic datasets and real datasets. Experimental results indicate that RECOME is able to discover clusters with different shapes, densities, and scales. It outperforms six baseline methods on both synthetic datasets and real datasets. Moreover, FJDD is shown to be effective to extract the jump discontinuity set of parameter $α$ for all tested datasets, which can ease the task of data exploration and parameter tuning.