The Kaczmarz algorithm is an iterative method for solving linear equations in the form of Ax  =  b. It is widely used in computed tomography and digital signal processing (DSP) but has yet to be adopted in computer-generated holography. Phase retrieval algorithms, such as Gerchberg–Saxton or Fienup, are significantly more popular in this field. However, we propose a unique and alternative approach to projecting a replay field through discrete Fourier transform matrices and have shown that there are legitimate benefits to implementing this approach. The gradient descent iteration mechanism adopted by Kaczmarz, for instance provides finer granularity control over the individual pixels in the replay field. We consequently demonstrate the quality of the image is significantly improved when compared with Gerchberg–Saxton.