  We propose a scheme to deterministically generate Greenberger-Horne-Zeilinger
states of $N\geq 3$ atoms trapped in spatially separated cavities connected by
optical fibers. The scheme is based on the technique of fractional stimulated
Raman adiabatic passage which is one-step in the sense that one needs just wait
for the desired entangled state to be generated in the stationary regime. The
parametrized shapes of the Rabi frequencies of the classical fields that drive
the two end atoms are chosen appropriately to realize the scheme. We also show
numerically that the proposed scheme is insensitive to the fluctuations of the
pulses' parameters and, at the same time, robust against decoherence caused by
the dissipation due to fiber decay. Moreover, a relatively high fidelity can be
obtained even in the presence of cavity decay and atomic spontaneous emission.
