Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation; however, it cannot be used to suppress coherent noise. This limitation results from the fact that the conventional MSSA method cannot distinguish between useful signals and coherent noise in the singular spectrum. We have developed a randomization operator to disperse the energy of the coherent noise in the time-space domain. Furthermore, we have developed a novel algorithm for the extraction of useful signals, i.e., for simultaneous random and coherent noise attenuation, by introducing a randomization operator into the conventional MSSA algorithm. In this method, which we call randomized-order MSSA, the traces along the trajectory of each signal component are randomly rearranged. Two ways to extract the trajectories of different signal components are investigated. The first is based on picking the extrema of the upper envelopes, a method that is also constrained by local and global gradients. The second is based on dip scanning in local processing windows, also known as the Radon method. The proposed algorithm can be applied in 2D and 3D data sets to extract different coherent signal components or to attenuate ground roll and multiples. Different synthetic and field data examples demonstrate the successful performance of the proposed method.