Multichannel single center (MCSC) method for the theoretical description of the electron continuum spectrum in molecules is reported. The method includes coupling between different continuum channels via electron correlations and describes, thereby, photoelectron continuum in the Tamm-Dancoff (configuration interaction singles) approximation. Basic equations of the non-iterative one-channel single center (SC) method and their extension to the MCSC method are presented, and an efficient scheme for their numerical solution is outlined. The method is tested on known illustrative examples of the Ar 3s-, HCl 4σ- and N2 1σ-photoionization processes, where inter-channel coupling plays a very important role. Unlike our previous SC studies, the present MCSC method can reliably be applied to photoionization of outer and valence molecular orbitals, where inter-channel correlations in continuum might be relevant.