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We construct the manifestly Lorenz-invariant formulation of the N=1 D=4 massive superparticle with tensorial central charges. The model contains a real parameter k and at possesses one -symmetry while at k=0 the number of -symmetry is two. The equivalence of the formulations at all is obtained. The local transformations of -symmetry are written out. It is considered the using of index spinor for construction of the tensorial central charges. It is obtained the equivalence at classical level between the massive D=4 superparticle with one -symmetry and the massive D=4 spinning particle

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