The algorism of indexing hexagoanal and tetragonal Debye-Scherrer photographs has been thoroughly discussed. It is pointed out that the procedure of finding a common solution for a series of Diophantine linear simultaneous equations, even for the low angle diffraction lines, seems to be untenable, because the solution is not unique.It is proposed that by adopting the same principle used in the new graphic method suggested by one of the authors, one may utilize three independent low angle sin2θ's and the density of the crystal, and form a series of conditional linear equations together with a series of equations representing equiatomic curves, a unique solution may be obtained which is the intersection of three conditional lines arising from different sin2θ's and one equiatomic curve. This gives the primary translations of the unit cell, and simultaneously the number of formula weight units contained therein.A computer program in FORTRAN has been written, the identification of which is POWDBX-HT. The time required to index one photograph is less than one minute.