Permutation arrays (PAs, or permutation codes) are useful in communication over power lines. Distance-increasing mappings (DIMs) from the set of binary vectors of a fixed length to the set of permutations of the same length that strictly increase Hamming distances (except when that is obviously not possible) are useful to construct permutation arrays. In this paper, we first give a new recursive construction of DIMs. Next, with a tricky and very different way to use the recursive construction of DIMs, we find a new construction of PAs. Finally, a new lower bound for the size of PAs is given.