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We use the decomposition of o(3,1)=sl(2;C)_1\oplus sl(2;C)_2 in order todescribe nonstandard quantum deformation of o(3,1) linked with Jordaniandeformation of sl(2;C}. Using twist quantization technique we obtain thedeformed coproducts and antipodes which can be expressed in terms of realphysical Lorentz generators. We describe the extension of the considereddeformation of D=4 Lorentz algebra to the twist deformation of D=4 Poincarealgebra with dimensionless deformation parameter.Comment: 6 pages, presented during the XIVth International Colloquium on  Integrable Systems (ISQS-14), Prague, June 16-18, 2005; to appear in Czech.  J. Phys. v.55 no. 11 (2005

On twist quantizations of D = 4 Lorentz and Poincare algebras