By using the electronic wave functions obtained from an ab initio calculation, including the spin-orbit coupling, the electronic transition moments have been investigated for two bound states of symmetry ⍀ ϭ 1/2 and ⍀ ϭ 3/2 of the molecular ion KRb ϩ . Based on a canonical functions approach for the determination of the vibrational wave functions, the matrix elements have been calculated for the bound states considered for v ϭ 0, 10, 20 with vЈ-v ϭ 0, 1, 2, . . . ,6; by using the same canonical approach, the eigenvalues and abscissas of the corresponding turning points (r min and r max ) have been investigated for these states that obtained from a theoretical ab initio calculation up to v ϭ 105.