Transformation of Relativistic Wave Equations

A unitary transformation is found which transforms the Dirac equation into two uncoupled equations. These involve higher orders of the time derivative than the first. In order ${\left(\frac{v}{c}\right)}^2$ the equations involve only the first time derivative and they are then equivalent to the Foldy-Wouthuysen transformation. While the equations are uncoupled and free of odd operators the functions satisfying them cannot be interpreted as different functions describing positive and negative energies separately, the general interpretation in the exact theory remaining in terms of the four-component wave function.