In a triclinic system, the squares of reciprocal spacings of any seven linearly independent X-ray powder lines which belong to the same lattice fulfill a Diophantine equation containing their Miller indices, which involves a 7 × 7 determinant. This can be expanded in minors which are integers. Theory is developed which breaks the problem of solving this equation into smaller steps, more easily amenable to numerical evaluation. The triclinic case has not yet been tried on a practical example, but the method has been already used in practice for systems of higher symmetry, for which the computational labor is much reduced.