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An appropriate generalization of the unitary parasupersymmetry algebra ofBeckers-Debergh to arbitrary order is presented in this paper. A specialrepresentation for realizing of the even arbitrary order unitaryparasupersymmetry algebra of Beckers-Debergh is analyzed by one dimensionalshape invariance solvable models, 2D and 3D quantum solvable models obtainedfrom the shape invariance theory as well. In particular in the specialrepresentation, it is shown that the isospectrum Hamiltonians consist of thetwo partner Hamiltonians of the shape invariance theory.Comment: 17 pages, LaTex2e, A new section added, To appear in IJMP

ON THE GENERALIZED UNITARY PARASUPERSYMMETRY ALGEBRA OF BECKERS–DEBERGH