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Using the complete orthonormal sets of radial parts of nonrelativitisticexponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor sphericalharmonics of rank s the new formulae for the 2(2s+1)-component relativisticspinors useful in the quantum mechanical description of the arbitraryhalf-integral spin particles by the generalized Dirac equation introduced bythe author are established in position, momentum and four-dimensional spaces,where 1/ 2, 3 / 2, 5 / 2, ... s = . These spinors are complete without theinclusion of the continuum. The 2(2s+1)component spinors obtained are reducedto the independent sets of two-component spinors defined as a product ofcomplete orthonormal sets of radial parts of orbitals and twocomponent spinortype tensor spherical harmonics. We notice that the new idea presented in thiswork is the unified treatment of half-integral spin and scalar particles inposition, momentum and four-dimensional spaces. Relations presented in thisstudy can be useful in the linear combination of atomic orbitals approximationfor the solution of different problems arising in the relativistic quantummechanics when the orthonormal basis sets of relativistic exponential typespinor wave functions and Slater type spinor orbitals in position, momentum andfour -dimensional spaces are employed.

New Complete Orthonormal Basis Sets of Relativistic Exponential Type  Spinor Orbitals and Slater Spinor Functions of Particles with Arbitrary  Half-Integral Spin in Position, Momentum and Four-Dimensional Spaces