  Four-dimensional Einstein-Maxwell-Dilaton theory admits asymptotically flat
extremal dyonic solutions for an infinite discrete sequence of the coupling
constant values. The quantization condition arises as consequence of regularity
of the dilaton function at the event horizon. These dyons satisfy the no-force
condition and have flat reduced three spaces like true BPS configurations, but
no supersymmetric embeddings are known except for some cases of lower values of
the coupling sequence.
