We have studied the coupling behavior of microphase separation and autophobic dewetting in weakly segregated poly(e-caprolactone)-block-poly(L-lactide) (PCL-b-PLLA) diblock co-polymer ultrathin films on carbon-coated mica substrates. At temperatures higher than the melting point of the PLLA block, the copolymer forms a lamellar structure in bulk with a long period of L similar to 20 nm, as determined using small-angle X-ray scattering. The relaxation procedure of ultrathin films with an initial film thickness of h = 10 nm during annealing has been followed by atomic force microscopy (AFM). In the experimental temperature range (100-140 degrees C), the co-polymer dewets to an ultrathin film of itself at about 5 nm because of the strong attraction of both blocks with the substrate. Moreover, the dewetting velocity increases with decreasing annealing temperatures. This novel dewetting kinetics can be explained by a competition effect of the composition fluctuation driven by the microphase separation with the dominated dewetting process during the early stage of the annealing process. While dewetting dominates the relaxation procedure and leads to the rupture of the ultrathin films, the composition fluctuation induced by the microphase separation attempts to stabilize them because of the matching of h to the long period (h similar to 1/2L). The temperature dependence of these two processes leads to this novel relaxation kinetics of co-polymer thin films.