  The paper discusses the mathematical consequences of the application of
derived variables in gauge fields. Physics is aware of several phenomena, which
depend first of all on velocities (like e.g., the force caused by charges
moving in a magnetic field, or the Lorentz transformation). Applying the
property of the second Noether theorem, that allowed generalised variables,
this paper extends the article by Al-Kuwari and Taha (1991) with a new
conclusion. They concluded that there are no extra conserved currents
associated with local gauge invariance. We show, that in a more general case,
there are further conserved Noether currents. In its method the paper
reconstructs the clue introduced by Utiyama (1956, 1959) and followed by
Al-Kuwari and Taha (1991) in the presence of a gauge field that depends on the
co-ordinates of the velocity space. In this course we apply certain (but not
full) analogies with Mills (1989). We show, that handling the space-time
coordinates as implicit variables in the gauge field, reproduces the same
results that have been derived in the configuration space (i.e., we do not lose
information), while the proposed new treatment gives additional information
extending those. The result is an extra conserved Noether current.
