  We carry out a direct, iterative Foldy--Wouthuysen transformation of a
general Dirac Hamiltonian coupled to an electromagnetic field, including the
anomalous magnetic moment. The transformation is carried out through an
iterative disentangling of the particle and antiparticle Hamiltonians, in the
expansion for higher orders of the momenta. The time-derivative term from the
unitary transformation is found to be crucial in supplementing the transverse
component of the electric field in higher orders. Final expressions are
obtained for general combined electric and magnetic fields, including strong
magnetic fields. The time-derivative of the electric field is shown to enter
only in the seventh order of the fine-structure constant if the transformation
is carried out in the standard fashion. We put special emphasis on the case of
strong fields, which are important for a number of applications, such as
electrons bound in Penning traps.
