It is shown here that the Cauchy problem for the Euler equations of a nonhomogeneous idealincompressible fluid has a unique solution for a small time interval. In comparison with the previous paper[1] and [2] in references, we discuss the problem under the weaker assumptions to given data, and showthe existence of a solution by means of a simple constructive procedure, namely, by proving that a suitablesequence of successive approximations converges.