  In the textbook proofs of Lorentz covariance of the Dirac equation, one
treats the wave function as a spinor and gamma matrices as scalars, leading to
a quite complicated formalism with several pedagogic drawbacks. As an
alternative, I propose to teach Dirac equation and its Lorentz covariance by
using a much simpler, but physically equivalent formalism, in which these
drawbacks do not appear. In this alternative formalism, the wave function
transforms as a scalar and gamma matrices as components of a vector, such that
the standard physically relevant bilinear combinations do not change their
transformation properties. The alternative formalism allows also a natural
construction of some additional non-standard bilinear combinations with
well-defined transformation properties.
