We report the observation of a strong anomaly in the magnetic-field dispersion of negatively charged excitons in dilute two-dimensional electron systems. The anomaly exists in an intermediate density range around 1x10(11) cm(-2), and at temperatures T<1 K, only. The strength of the anomaly at T=0.1 K is about 2.5 meV, and the most striking feature is that it can be completely destroyed by a small thermal energy of about 0.2 meV (2 K). Furthermore, the anomaly is observed both in photoluminescence and direct absorption measurements, which gives a strong indication that it is of intrinsic origin.