The present invention relates to a method for determining a minimum determinant to determine a generator matrix for designing an optimum space-time trellis codes (STTC) of multiple transmit and receive antennas, comprising the steps of: first, generating a plurality of random generator matrices; then, obtaining minimum determinant; and then, determining the generator matrix by selecting the generator matrix having the highest value of the minimum determinant; wherein getting minimum determinant for each generator matrix characterized by the steps of: first, converting the generator matrix into a trellis state diagram; then, converting the trellis state diagram into a tree structure; then, generating only node 0 at last layer of the tree structure; then, eliminating a descendant node if the descendant node has same state with a parent node; then, calculating determinant only at all node 0; then, obtaining the minimum determinant.