N= 4 irreducible scalar superflelds

The N = 4 extended supersymmetry in four-dimensional space-time is considered from the viewpoint of the two included N = 2 extended supersymmetries. Using the results for the structure of the irreducible superfields in N = 2 superspace obtained earlier the task of explicit construction of N = 4 irreducible superfields with SU(2) X SU(2) internal symmetry in N = 2X2 superspace is solved. The decomposition of the N = 4 scalar superfield into N = 4 irreducible ones is described and the rules for collecting the irreducible scalar N = 2X2 superfields with SU(2) X SU(2) internal symmetry into N = 4 irreducible scalar superfields with SU(4) internal symmetry are set. To illustrate this method a simple consistent way of constructing the linearized off-shell N = 4 conformal supergravity in N = 4 superspace is shown.