This paper proposes a new method to generate quadriphase sequences to be used in Code Division Multiple Access systems. Starting from a set of prototype binary sequences with good properties of their correlation functions, a set of quadriphase sequences is produced by transforming each binary element of the prototype sequences into a quadriphase element of the new sequence. The correlation functions of the new set are shown to have smaller absolute values than the original ones, if the length of the sequence is odd. The absolute values of the periodic and odd correlation functions of the quadriphase sequences are limited by identical upper bounds, which depend on the bounds for the set of binary sequences. Cyclic shifting of the original sequences may yield a further reduction of the maximum values of the odd and periodic correlation functions, as shown by computer calculations.