<p>We present a new method to calculate analytically the roots of the general complex polynomial of degree four. This method is based on the approach of appropriate changes of variable involving arbitrary parameters. The advantage of this method is to calculate the roots of the quartic polynomial as closed formula using the standard convention of the square and cubic roots. In contrast, the reference methods for this problem, as Ferrari, Lagrange, Descartes and Euler, give the roots of the quartic polynomial as expressions required a root of a cubic equation, called resolvent cubic of the fourth degree equation, given in terms of cubic roots with case distinctions which require a convention of roots depending on coefficients.</p>