More on BPS States in N=4 Supersymmetric Yang-Mills Theory on R x S3

We perform a systematic analysis on supersymmetric states in N = 4 supersymmetric Yang-Mills theory (SYM) on R x S-3. We find a new set of 1/16 BPS equations and determine the precise configuration of the supersymmetric states by solving all 1/16 BPS equations when they are valued in Cartan subalgebra of a gauge group and the fermionic fields vanish. We also determine the number of supersymmetries preserved by the supersymmetric states varying the parameters of the BPS solutions. As a byproduct we present the complete set of such supersymmetric states in N = 8 SYM. on R x S-2 by carrying out dimensional reduction.