We discuss the condition under which a pair of closely lying levels, w
hen coupled to a fourth level via a single-laser field, exhibit popula
tion trapping without decay to a lower level. In the discussion, the d
ecay between the pair and the fourth level is taken into account. When
the fourth level is lower than the pair, the condition for population
trapping in the pair can be satisfied under arbitrary laser intensity
by adjusting the laser detuning. When the fourth level is above the p
air, population trapping in the pair is impossible when the decay from
the fourth level to the pair is included. The influence of the decay
between the pair and the fourth level on the spontaneous spectrum from
the pair to the lower level is also studied.