The discovery of nearest neighbors, without training in advance, has many applications, such as the formation of mosaic images, image matching, image retrieval and image stitching. When the quantity of data is huge and the number of dimensions is high, the efficient identification of a nearest neighbor (NN) is very important. This study proposes a variation of the KD-tree - the arbitrary KD-tree (KDA) - which is constructed without the need to evaluate variances. Multiple KDAs can be constructed efficiently and possess independent tree structures, when the amount of data is large. Upon testing, using extended synthetic databases and real-world SIFT data, this study concludes that the KDA method increases computational efficiency and produces satisfactory accuracy, when solving NN problems.