Flow disturbances can significantly affect flow metering because the downstream flow of flow disturbances can become unstable and asymmetric, thus resulting in measurement errors in the flow meter. A clamp-on type ultrasonic flow meter is an example of a flow meter that is susceptible to flow disturbances given its diametrical configuration of ultrasonic paths. Several flow rate correction formulas have been suggested to mitigate the effect of flow disturbance for improved flow metering. As a novel method, a multi-dimensional non-linear correction formula is suggested to overcome limitations in flow metering that are attributed to the non-linearity of flow disturbances. The non-linear correction formula comprises n-th order polynomials with multiple variables. To validate the usefulness of the non-linear correction formula, the standard error of estimate (SEE) is introduced. Four types of flow configurations, namely, downstream of a contraction pipe, an expansion pipe, a single elbow joint, and a tee joint, are used to show the effect of the non-linear correction formula. The expanded uncertainty based on the SEE indicates estimated values of 1.29%, 11.14%, 1.07%, and 6.31% for the four upstream flow configurations, respectively. Thus, the effect of the non-linear correction formula is limited according to the upstream flow conditions. In the downstream flow of the contraction pipe and of the single elbow joint, the non-linear correction formula not only harmonizes the distribution of the flow rate deviations but also removes the biases of flow rate deviations with respect to the flow velocity, the installation location, and the diameter ratio.