Every time-series has its own linear trend, the directionality of a time-series, and removing the linear trend is crucial to get more intuitive matching results. Supporting the linear detrending in subsequence matching is a challenging problem due to the huge number of all possible subsequences. In this paper we define this problem as the linear detrending subsequence matching and propose its efficient index-based solution. To this end, we first present a notion of LD-windows (LD means linear detrending). Using the LD-windows we then present a lower bounding theorem for the index-based matching solution and show its correctness. We next propose the index building and subsequence matching algorithms. We finally show the superiority of the index-based solution.