The relationship between the coherency matrix of arbitrary orthogonal basic vectors and their coordinates in the Stokes space is studied. It is revealed that the coherency matrix of different basic vectors can be concisely represented by their coordinates in the Stokes space. On this basis, a new method to directly measure the Jones matrix of an optical device is proposed and verified experimentally with a Faraday rotator. The Jones matrix of arbitrary basic vectors can be obtained without any transformation between the Stokes vectors and the Jones vectors, or between the Muller matrices and the Jones matrices. This provides a more convenient way to measure the polarization properties of optical devices and analyze the polarization performance of optical loops.