The colossal magnetoresistance (CMR) effect of manganites is widely believed to be caused by the competition between a ferromagnetic (FM) metallic state induced by the double-exchange mechanism and an insulator with complex spin, charge, and orbital order. Recent computational studies in small clusters have indeed reported a CMR precisely near the frontier between those two states at a realistic hole density x=1/4. However, the detailed characteristics of the competing insulator were not fully understood in those previous investigations. This insulator is expected to display special properties that lead to the CMR; otherwise any competition between ferromagnetic and antiferromagnetic states would induce such an effect, which is not the case experimentally. In this report, the competing insulator at electronic density x=1/4 and in the CMR regime is studied in detail using the double-exchange two-orbital model with Jahn-Teller lattice distortions on two-dimensional clusters, employing a careful large-scale cooling down process in the Monte Carlo simulations to avoid being trapped in metastable states. Our investigations show that this competing insulator has an unexpected complex structure, involving diagonal stripes with alternating regions displaying FM and CE-like order. The level of complexity of this new state even surpasses that of the recently unveiled spin-orthogonal-stripe states and their associated high degeneracy. This new state complements the long-standing scenario of phase separation, since the alternating FM-CE pattern appears even in the clean limit. The present and recent investigations are also in agreement with the many “glassy” characteristics of the CMR state found experimentally, due to the high degeneracy of the insulating states involved in the process. Results for the spin-structure factor of the new states are also here provided to facilitate the analysis of neutron scattering experiments for these materials.