We have prepared a novel series of banana-shaped molecules with a central bent core based on a 2,7-dihydroxynaphthalene group, the side wings containing a Schiff's based moiety, and alkoxy flexible tails with carbon numbers n = 6, 8, 10, 12, 14, and 16. Among these, the molecules with n = 8-16 formed a novel smectic phase. Its smectic layer possessed a liquidlike association of the molecules similar to the SmA or SmC phase, although the texture that developed from the isotropic melt was unconventional. Small fractal domains initially grew and then coalesced into several large domains. Very weak birefringence and fine structure without any anisotropy are characteristic of this phase. It is interesting to note that two different domains exist showing the opposite sign of optical rotation. Strong circular dichroism (CD) with a peak at 430 nm was also observed for each domain with the opposite sign. The results suggest a natural occurrence of the helix in these materials. The right-handed and left-handed helices were formed with equal probabilities, but the left-handed helix was selectively formed by the introduction of a chiral dopant. The molecule with n = 6 formed a frustrated smectic phase, which exhibited a simple fan-shaped texture.