The transition probabilities for individual and multiplet lines between some excited levels of atomic potassium are calculated using weakest bound electron potential model theory (WBEPMT). The numerical nonrelativistic Harteee-Fock wave functions for the expectation values of radii in all excited states, unlike the Numerical Coulomb Approximation method traditionally used for WBEPMT and experimental ionization energies, have been employed to determine the parameters. The results obtained during this work agree very well with the accepted values taken from National Institute Standards and Technology. Moreover, some transition probabilities not existing on the data bases for highly excited levels in atomic potassium have been obtained using this method. © 2008 NRC Canada.