  In this work we consider morphisms that preserve well-known non-repeating
properties: squarefreeness, cubefreeness, overlap-freeness and weak
squarefreeness. Up to the present moment only the morphisms preserving three
out of four non-repeating properties have been known. The problem of the
existence of weakly squarefree morphisms was open.
  The essential result of this work is the positive solution to this problem.
An example of the morphism preserving all four properties is provided. Also, it
is proved that there are no morphisms with the same properties and a lower
rank.
