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Properties of tensors equivalent to the direct product of two different4-spinors are investigated. It is shown that the tensors obey additional 8nonlinear restrictions, those are presented in Lorentz covariant form. In thecontext of the Dirac-K\"{a}hler theory, such a property can be interpreted asfollows: if one wishes to consider the Dirac-K\"{a}hler field as consisting oftwo 4-spinor fields, one must impose additional restrictions on tensors of theDirac-K\"{a}hler field, which leads to a non-linear wave equation for a complexboson field (composed on the base of two 4-spinor fields). Instead, the use offour bi-spinor fields gives possibility to construct the Dirac-K\"{a}hlertensor set of 16 independent components. However, the formulas relating theDirac-K\"{a}hler boson to four fermion fields are completely different fromthose previously used in the literature. In explicit form, restrictions on four4-spinor corresponding to separation of different simplest bosons with spin 0or 1 and various intrinsic parities, are constructed.

Some Consequences from the Dirac-Kahler Theory: on Intrinsic Spinor Sub-structure of the Different Boson Wave Functions