  Global existence and boundedness of solutions to the Cauchy problem for the
four dimensional fully parabolic chemotaxis system with indirect signal
production are studied. We prove that solutions with initial mass below
$(8\pi)^2$ exist globally in time. This value $(8\pi)^2$ is known as the four
dimensional threshold value of the initial mass determining whether blow-up of
solutions occurs or not. Furthermore, some condition on the initial mass
guaranteeing that the solution remains uniformly bounded is also obtained.
