This paper discussed the local control of interpolating function by using rational quartic spline (quartic/linear) with one parameter αi > 0. The rational spline has C1 continuity and it is unique for each αi The bounded property of the rational quartic spline is discussed in details. Later, the rational quartic spline will used for value point control to generate the interpolating curves. We gives the condition on the possible choices of P(t) = N might be. By having the range for N there is no need to solve the equation to find the positive value of parameter. Comparisons with the existing scheme also have been done. From all numerical results, the local control interpolation by using rational quartic spline interpolant (quartic/linear) gives satisfactory results. © 2014 Samsul Ariffin Abdul Karim and Kong Voon Pang.