We introduce a novel non-dimensional "intrinsic layer-line spacing" concept for electron diffraction analysis of single-walled carbon nanotubes (SWCNTs). Accordingly, we develop a unique method for direct determination of chiral indices (n, m) of the carbon nanotubes from their electron diffraction patterns (EDPs). The new method is totally calibration-free. Errors due to the nanotube inclination are specified. The tilt angle of the carbon nanotube with respect to the incident electron beam is simultaneously evaluated, thus the effect of the tube tilting is compensated for in the (n, m) determination. Several effective procedures are proposed to cross-check the results by using abundant information contained in the diffraction patterns. The efficiency of the method is demonstrated on both simulated and experimental diffraction patterns from single-walled nanotubes. The technique can be extended to structural analysis of nanotubes of structure similar to carbon nanotubes, such as boron nitride nanotubes.