In data streams or web scenarios at highly variable and unpredictable rates, a good join algorithm should be able to "hide" the delays by continuing to output join results. The non-blocking algorithms allow some tuples to be flushed onto disk, with the goal of producing results continuously when data transmission is suspended. But state-of-the-art algorithms have trouble with the constraint of allocated memory. To make better use of memory, a novel non-blocking join algorithm based on hash-merge for improving query response times is proposed. The reduced data structure of in-memory tuples helps to improve memory utility. A replacement selection tree is applied to adjust memory by expanding or shrinking the size of the tree and separates one external join transaction into multi-subtasks. In addition, a cost model to estimate task output rate is proposed to select the in-disk portion that promises to produce the fastest results in the external join stage. Experiments show that the technique, with far less memory, delivers results faster than the three non-blocking join algorithms (XJoin, HMJ and RPJ), with up to almost two-fold improvement in reliable network and one order of magnitude improvement in unreliable network in terms of the number of the reported tuples.