The number of real-time information sources, or so-called streams, has rapidly increased, leading to a greater demand for complex analyses over streams. Although many stream analysis methods exist, aggregation is fundamental to ascertain higher levels of knowledge from raw data. In particular, sliding-window aggregation, where aggregations over sliding windows are repeatedly computed, is useful in many real-life applications. Two stacks is the state-of-the-art method to compute sliding-window aggregations incrementally with a O(1) time complexity. However, its performance seriously degrades as the window size increases due to the high overhead to maintain its index. To address this problem, this paper proposes a linear bidirectional index (L-BiX) that exploits two kinds of partial aggregations. Specifically, forward (old-to-new) and backward (new-to-old) aggregations allow efficient computations in an incremental manner. The proposed algorithm requires the same time complexity as two stacks (O(1)). Our experimental evaluation shows that the throughput of L-BiX can be faster by up to 1.71 times than that of two stacks with a 50% smaller memory footprint.