  An exact solution of the current-free Einstein-Maxwell equations with the
cosmological constant is presented. The solution is of Petrov type D, includes
the negative cosmological constant, and could be a ``background addition'' to
the present-day models of the universe. It has a surprising property such that
its electromagnetic field and cosmological constant are interdependent (this
constant is proportional to the energy density of this field), which may
suggest a new way of measuring the constant in question. The solution describes
a constant electromagnetic background with a preferred direction in the
universe, and defines the entire lifetime of the universe as a simple function
of the negative cosmological constant. According to our solution the absolute
value of this constant should be considerably lower than that recently
estimated, when astrophysical data are taken into account. Our solution is a
special case of that published by Bertotti in 1959. His solution (in terms of
which the cosmological constant and the background electromagnetic field are
independent) and its two other special cases, i.e. the conformally flat
Robinson solution (1959) and the one which is the counterpart of our solution
with the positive cosmological constant, are briefly discussed.
