An analytic formula is developed for calculating the generalized NMR order parameters in a protein from the normal mode analysis (NMA), The generalized order parameter, (S) over tilde(2), is given as thermal ensemble average of a Taylor series in powers of Delta, the displacement of internuclear vector from its mean. Henry and Szabo developed a method to calculate the ensemble average based on the NMA carried out in the Cartesian coordinate space (CCS), However, atomic motions in each individual CCS normal modes are linear in the three-dimensional space, which may cause interatomic distances even between covalently bonded atoms to change significantly. In this situation Henry and Szabo proposed to use a special formula for (S) over tilde(2) which includes a trick to compensate such changes. We showed that by carrying out the NMA in the dihedral angle space (DAS) and by interpreting each DAS normal mode into curved atomic motions, (S) over tilde(2) can be calculated reliably for spin pairs separated up to about 10 intervening covalent bonds by a natural formula without any trick.