  We present a sufficient condition of the complete position flocking theorem
for the Cucker-Smale type model on the unit sphere with an inter-particle
bonding force. For this second order dynamical system derived in [Choi, S.-H.,
Kwon, D. and Seo, H.: Cucker-Smale type flocking models on a sphere. arXiv
preprint arXiv:2010.10693, 2020] by using the rotation operator in three
dimensional sphere, we obtain an exponential decay estimate for the diameter of
agents' positions as well as time-asymptotic flocking for a class of initial
data. The sufficient condition for the initial data depends only on the
communication rate and inter-particle bonding parameter but not the number of
agents. The lack of momentum conservation and the curved space domain make it
difficult to apply the standard methodology used in the original Cucker-Smale
model. To overcome this and obtain a uniform position alignment estimate, we
use an energy dissipation property of this system and transform the
Cucker-Smale type flocking model into an inhomogeneous system of differential
equations of which solution contains the position and velocity diameters. The
coefficients of the transformed system are controlled by the communication rate
and a uniform upper bound of velocities obtained by the energy dissipation.
