Summary: We examine unsteady channel flows for different Reynolds numbers and for different configurations by extending a shooting method which was previously used to obtain a travelling-wave solution. A general initial condition is considered. We find a periodic-like solution to incompressible Navier-Stokes equations in a minimal flow unit. One cycle of the solution consists of two typical intervals: a single-streak period, and a double-streak period. The solution seems to be periodic; however, it cannot be distinguished from a heteroclinic cycle which consists of two heteroclinic orbits connecting two single-streak solutions, because the solution is tracked only for one and half periods.