  The photoion spectrum of atomic potassium was measured over the 3s -> np
excitation region with the photoion time-of-flight method and monochromatized
synchrotron radiation. An unusual spectrum with paired windows structure was
found instead of a simple regular Rydberg series. Such subsidiary windows have
not been observed in the 3s -> np resonances of Ar, which has a closed outer
shell. Based on Dirac-Fock calculations, the dual window structure at 36.7 eV
and at 37.4 eV was assigned to the 3s^{-1}3p^{6}4s4p resonance. The line shape
can be fitted by Fano's formula and the Fano parameters were obtained.
