Using high-resolution small-angle X-ray scattering, we observed a new type of the columnar phase with a simple rectangular (R(S)) structure in colloidal goethite dispersions. Furthermore, it displays a martensitic transition into the usual centered rectangular (R(C)) structure in an external magnetic field. The findings are rationalized in terms of entropic effects within a simple cell model. We interpret the results as an effect of the particle shape and the available degrees of freedom on the delicate balance between the space available for particle translations and rotations within the two structures.