  The Knill-Laflamme-Milburn (KLM) states have been proved to be a useful
resource for quantum information processing [Nature 409, 46 (2001)]. For atomic
KLM states, several schemes have been put forward based on the time-dependent
unitary dynamics, but the dissipative generation of these states has not been
reported. This work discusses the possibility for creating different forms of
bipartite KLM states in neutral atom system, where the spontaneous emission of
excited Rydberg states, combined with the Rydberg antiblockade mechanism, is
actively exploited to engineer a steady KLM state from an arbitrary initial
state. The numerical simulation of the master equation signifies that a
fidelity above 99\% is available with the current experimental parameters.
