A new type of non-linear, chain reacting instability is presented that a sequential condensation occurs in a thermally unstable interstellar CO cloud, triggered by a local density perturbation. Non-linear growth of the instability was followed numerically with a one-dimensional and slab symmetric hydrodynamical code. The result shows that a local, small density enhancement onto initial density of n0=510 cm−3 around x=0 (x: spatial coordinate) grows to a maximum density of nmax=1300 cm−3 in a time scale of 0.6×106y, and at the same time the gas in neighbouring region at x=0.1–0.2 pc shifts into a low-density phase of nmin=200 cm−3. Since we assume a constant heating per particle by photons and cosmic rays, the gas in low density region is relatively more heated so that the pressure therein becomes higher than the background pressure. Then the low density gas pushes its neighbouring gas foward increasing x to lead to a second density enhancement at x=0.2 pc. In this way many further condensations are produced in a sequential manner. The spacings and sizes of condensations are uniquely determined by the characteristic parameters, the growth time of instability and the sound velocity of the background gas alone. The present calculation gives the spacing, 0.24 pc, and the mass of each fragment, 0.2M⊙. This mechanism could be related to sequential formation of less-massive stars in interstellar CO clouds, if the condensations evolve further into star formation sites.