In the first part of the paper, flow diagrams are introduced to represent inter ah mappings of a set into itself. Although not every diagram is decomposable into a finite numbm of given base diagrams, this becomes hue at a semantical level due to a suitable extension of the given set and of the basic mappings defined in it. Two normalization methods of flow diagrams are given. The first has |hree base diagrams; the second, only two.In the second part of the paper, the second method is applied to 'lhe theory of Turing machines. With every Turing maching provided with a two-way half-tape, ihere is associated a similar machine, doing essentially 'lhe same job, but working on a tape obtained from the first one by interspersing alternate blank squares. The new machine belongs to the family, elsewhere introduced, generated by composition and iteration from the two machines X and R. That family is a proper subfamily of the whole family of Turing machines.

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