The complex orthogonal designs (CODs) with maximal rates and minimal decoding delays is a open problem for space-time block code (STBC). We prove the open problem in the minimal decoding delays, and we present an odd transmit antennas CODs of STBC, associate with Liang's padding scheme or Su's systematic design method we can get a complete designs for CODs of STBC with maximal rates and minimal decoding delays base on the previous fruit in this field. Hence, we give a better answer for the open problem