A curve interpolation scheme with C1 continuity is developed by using rational quartic Said-Ball function with quartic numerator and linear denominator. The scheme has a unique representation, with one shape parameter that can be used to change the shape of the curve. Sufficient conditions for the monotonicity of the rational interpolant have been derived. Several numerical results are given to show the capability of the presented scheme. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.