Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on a method to improve the accuracy of polynomial evaluation via Horner’s scheme. Such an algorithm exists for polynomials with real floating point coefficients. In this paper, we provide a new algorithm which deals with polynomials with complex floating point coefficients. We show that the computed result is as accurate as if computed in twice the working precision. The algorithm is simple since it only requires addition, subtraction and multiplication of floating point numbers in the same working precision as the given data. Such an algorithm can be useful for example to compute zeros of polynomial by Newton-like methods.