Before we demonstrate with examples how the new method is used to expand determinants, it is fitting that we briefly discuss the major advantage of this method over Chi`o method. In the new method, the elements needed to form any 2nd order determinant during condensation are elements from two consecutive rows. Whereas, in Chi`o method, the elements needed to form any 2nd order determinant are row 1 elements, and elements from any other row. Thus, in Chi`o method there is increasing difficulty in tracing the elements of each 2nd order determinant as the order of the original determinant increases. Let us now demonstrate with examples how the new condensation method is used to hand-evaluate