<p>Using the example of a Dirac particle in external static fields, Dirac theory is formulated as a single-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator is “split” into two two-component operators: one bounded below (in the nonrelativistic limit, it coincides with the Pauli operator), and the other bounded above. In the two-component formulation, exact analytical expressions are obtained for all observables, including the Dirac Hamiltonian, which are then investigated in the nonrelativistic and ultrarelativistic limits. A general solution to the equation for the unit two-component spinor describing a free particle is presented. The proposed formulation is compared with the original Foldy-Wouthuysen (FW) formalism, as well as with the exact FW formalism based on the “wave function reduction condition”.</p>