Let X be an infinite set and let φ be a given mapping of it into itself. We consider the C*-algebra Cφ(X) with a single generating element Tφ on Hilbert space l2(X). We show that Cφ(X) is isomorphic to C*-algebra generated by a finite set of partial isometries of a special kind if Tφ is continuous. We give the full description of Cφ(X) in case φ is injective mapping. Also we give the examples of Cφ(X) if φ is not injective.