Hadamard products of power series was first introduced and studied by Hadamard in 1899. According to Hadamard's multiplication theorem, the Hadamard product of two rational power series is still rational. Hadamard products have many applications including functional transcendence in number theory and zeta functions of graphs in combinatorics. In this work, we present several algorithms for computing the Hadamard products of two rational functions and describe a class of rational functions whose Hadamard square have only one pole.