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This paper proposed a fast and accurate computational method to determine the available transfer capability (ATC) in a power system. The methodology utilizes the curve fitting technique so-called as the cubic-spline interpolation technique that is incorporated into the Ralston's method in order to provide fast and accurate estimation of ATC. The Ralston's method is used to predict the two trajectory points of voltage magnitude and power flow. The cubic-spline interpolation technique is then used to accurately trace the P-V or P-S curves between two points of trajectory. The P-V and P-S curves represent as the voltage magnitude and power flow that varies with the increase of ATC. The value of ATC is then determined at the point where the voltage or the power flow limits intersect the curves. The effectiveness of the proposed method is verified by illustrating the ATC evaluation on a Malaysian power system. The ATC results that obtained from the proposed method are satisfactorily accurate and faster than the ATC evaluation using the recursive AC power flow computations.