This letter presents a novel, computationally-efficient interpolation method that has been optimised for use in ECG baseline drift removal. In our previous work 3 isoelectric baseline points per heart beat are detected, and here utilised as interpolation points. As an extension from linear interpolation, our algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus the algorithm produces a linear curvature that is computationally efficient while avoiding overshoots on nonuniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05Hz to 0.7Hz and also validated with real baseline wander data acquired from the MIT-BIH Noise Stress Database. The synthetic data results show an RMS error of 0.9μV (mean), 0.63μV (median) and 0.6μV (std. dev.) per heart beat on a 1mVp-p 0.1Hz sinusoid. On real data we obtain an RMS error of 10.9μV (mean), 8.5μV (median) and 9.0μV (std. dev.) per heart beat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7μV, 11.6μV (mean), 7.8μV, 8.9μV(median) and 9.8μV, 9.3μV (std. dev.) per heart beat respectively.