NMR shift arising from the electron orbital angular momentum and the electron spin dipolar-nuclear spin angular momentum interactions has been investigated for a $4d^{1}$ system in a strong crystal field of octahedral symmetry. To examine the NMR shif for a $4d^{1}$ system in a strong crystal field of octahedral symmetry, we derive a general expression for ${Delta}$B/B using a nonmultipole expansion technique. From this expression all the multipolar terms are determined. For the $4d^{1}$ system in a strong crystal field of octahedral symmetry the exact solution for NMR shift, ${Delta}$B, is compared with the multipolar results. ${Delta}$B/B for the $4d^{1}$ system is also compared with that for the $3d^{1}$ system. It is found that the $1/R^{7}$ term contributes dominantly to the NMR shift. However, there is good agreement between the nonmultipole and multipolar results for R-values larger than 0.2 nm for the $4d^{1}$ system but for R-values larger than 0.4 nm for the $3d^{1}$ system.