As one of the most useful online processing techniques, the theta-join operation has been utilized by many applications to fully excavate the relationships between data streams in various scenarios. As such, constant research efforts have been put to optimize its performance in the distributed environment, which is typically characterized by reducing the number of Cartesian products as much as possible. In this article, we design and implement a novel fast theta-join algorithm, called Prefap, by developing two distinct techniques - prefiltering and amalgamated partitioning-based on the state-of-the-art FastThetaJoin algorithm to optimize the efficiency of the theta-join operation. Firstly, we develop a prefiltering strategy before data streams are partitioned to reduce the amount of data to be involved and benefit a more fine-grained partitioning. Secondly, to avoid the data streams being partitioned in a coarse-grained isolated manner and improve the quality of the partition-level filtering, we introduce an amalgamated partitioning mechanism that can amalgamate the partitioning boundaries of two data streams to assist a fine-grained partitioning. With the integration of these two techniques into the existing FastThetaJoin algorithm, we design and implement a new framework to achieve a decreased number of Cartesian products and a higher theta-join efficiency. By comparing with existing algorithms, FastThetaJoin in particular, we evaluate the performance of Prefap on both synthetic and real data streams from two-way to multiway theta-join to demonstrate its superiority.