We investigated the ultrastructure of the secondary layer of the calcite shell of the terebratulide brachiopod Megerlia truncata with SEM and electron beam backscattering diffraction. The material of the secondary layer is an inorganic/organic fibre composite. Each individual cell of the outer epithelium secrets a single crystal confined in a protein sheath. The morphological fibre axes of the single crystals are almost parallel to the shell surface. The fibrous growth occurs in arbitrary directions perpendicular to the <0001> triad symmetry direction of calcite. Accordingly, the fibres form a cylindrical <0001> “fibre” texture, with the texture axis perpendicular to the shell surface. The curvature of the fibres is caused by lateral displacements or rearrangements of the secreting cell array during growth. In these events the existing crystal lattice is not distorted - it is the substrate for continued crystal growth from the cell, irrespective of direction.