Interpolation using Hermite polynomial cubic splines is well known and often used. Here we propose an approximation with the non-polynomial splines with the fourth order of approximation. The splines uses the values of the function and the first derivative of the function in the nodes. We call the approximation as first level approximation because it uses the first derivative of the function. This approximation has the properties of polynomial and trigonometric functions. Here we also have constructed a non-polynomial interpolating spline which has continuous the first and second derivative. This approximation uses the values of the function at the nodes and the values of the first derivative of the function at the ends of the interval [a, b]. Estimates of the approximations are given and the constants included in them are calculated. Numerical examples are given.