Introduction Several algorithms for the systematic generation of the permutations of n marks have been published. Recently Ord-Smith  has reviewed them. However, almost all of them are intended to generate all the n! arrangements. Corresponding to each member of the set of n! possible arrangements, there is another member such that one read from left-to-right and the other read from right-to-left are identical• We shall call them "reflections" of each other. The set of n!/2 permutations of n marks with the property that the reflection of any member is not included in the set may be called a "reflection-free" set of permutations of the marks. The generation of such reflection-free sets of permutations is fundamental to some problems such as scheduling problems. In this note we show how the adjacent transposition algorithms [2, 3, 4] can be used to generate reflection-free permutations and rosary permutat ions very efficiently. Rosary permutat ions have been discussed in detail by Harada .