A method for manufacturing endless material for security elements (12; 16) having micro-optical moiré magnification arrangements that exhibit a motif grid composed of a plurality of micromotif elements and a focusing element grid composed of a plurality of microfocusing elements for moiré-magnified viewing of the micromotif elements, in which a) a motif grid composed of an at least locally periodic arrangement of micromotif elements in the form of a first two-dimensional lattice is provided, b) a focusing element grid composed of an at least locally periodic arrangement of a plurality of microfocusing elements in the form of a second two-dimensional lattice is provided, - wherein the first and/or second lattice exhibits a hexagonal lattice symmetry or the symmetry of a parallelogram lattice, and is, in addition to the orientation of the lattice vectors with respect to each other, determined by a fixed orientation of the lattice to the endless material, especially to the longitudinal axis thereof, and wherein each lattice from the class of two-dimensional Bravais lattices with hexagonal lattice symmetry or the symmetry of a parallelogram lattice having a fixed orientation from 0-360° is selectable as the first and/ or second lattice, c) a pattern repeat of the motif grid and/or of the focusing element grid on the endless material is specified, d) it is checked whether the lattice of the motif grid and/or the lattice of the focusing element grid repeats periodically in the specified pattern repeat, and if this is not the case, a linear transformation is determined that distorts the first and/or the second lattice such that it repeats periodically in the specified pattern repeat, and e) for the further manufacture of the endless material, the motif grid or the focusing element grid is replaced by the motif grid that is distorted by the determined linear transformation, or the focusing element grid that is distorted by the determined linear transformation, wherein in step c), a pattern repeat q along the endless longitudinal direction of the endless material is specified, and wherein in step d), a lattice point P of the first and/or the second lattice is selected that lies near the endpoint Q of the vector 0 q given by the longitudinal pattern repeat, and a linear transformation V is determined that maps P to Q. a) a motif grid composed of an at least locally periodic arrangement of micromotif elements in the form of a first two-dimensional lattice is provided, b) a focusing element grid composed of an at least locally periodic arrangement of a plurality of microfocusing elements in the form of a second two-dimensional lattice is provided, - wherein the first and/or second lattice exhibits a hexagonal lattice symmetry or the symmetry of a parallelogram lattice, and is, in addition to the orientation of the lattice vectors with respect to each other, determined by a fixed orientation of the lattice to the endless material, especially to the longitudinal axis thereof, and wherein each lattice from the class of two-dimensional Bravais lattices with hexagonal lattice symmetry or the symmetry of a parallelogram lattice having a fixed orientation from 0-360° is selectable as the first and/ or second lattice, - wherein the first and/or second lattice exhibits a hexagonal lattice symmetry or the symmetry of a parallelogram lattice, and is, in addition to the orientation of the lattice vectors with respect to each other, determined by a fixed orientation of the lattice to the endless material, especially to the longitudinal axis thereof, and wherein each lattice from the class of two-dimensional Bravais lattices with hexagonal lattice symmetry or the symmetry of a parallelogram lattice having a fixed orientation from 0-360° is selectable as the first and/ or second lattice, c) a pattern repeat of the motif grid and/or of the focusing element grid on the endless material is specified, d) it is checked whether the lattice of the motif grid and/or the lattice of the focusing element grid repeats periodically in the specified pattern repeat, and if this is not the case, a linear transformation is determined that distorts the first and/or the second lattice such that it repeats periodically in the specified pattern repeat, and e) for the further manufacture of the endless material, the motif grid or the focusing element grid is replaced by the motif grid that is distorted by the determined linear transformation, or the focusing element grid that is distorted by the determined linear transformation, wherein in step c), a pattern repeat q along the endless longitudinal direction of the endless material is specified, and wherein in step d), a lattice point P of the first and/or the second lattice is selected that lies near the endpoint Q of the vector 0 q given by the longitudinal pattern repeat, and a linear transformation V is determined that maps P to Q.