A new learning algorithm for speech separation networks is designed to explicitly reduce residual noise and artifacts in the separated signal in an unsupervised manner. Generative adversarial networks are known to be effective in constructing separation networks when the ground truth for the observed signal is inaccessible. Still, weak objectives aimed at distribution-to-distribution mapping make the learning unstable and limit their performance. This study introduces the remix-cycle-consistency loss as a more appropriate objective function and uses it to fine-tune adversarially learned source separation models. The remix-cycle-consistency loss is defined as the difference between the mixed speech observed at microphones and the pseudo-mixed speech obtained by alternating the process of separating the mixed sound and remixing its outputs with another combination. The minimization of this loss leads to an explicit reduction in the distortions in the output of the separation network. Experimental comparisons with multichannel speech separation demonstrated that the proposed method achieved high separation accuracy and learning stability comparable to supervised learning.