In the superalgebraic representation of spinors using Grassmann densities and the corresponding derivatives, we introduce a generalization of Dirac conjugation, and this generalization yields Lorentz-covariant transformations of conjugate spinors. The signature of the generalized gamma matrices, the number of them, and the decomposition of second quantization with respect to momenta are given by a variant of the generalized Dirac conjugation and by the requirement that the algebra of canonical anticommutation relations should be preserved under transformations of spinors and conjugate spinors.