  In this paper we study the BMS symmetry of the celestial OPE of two positive
helicity gravitons in Einstein theory in four dimensions. The celestial OPE is
obtained by Mellin transforming the scattering amplitude in the (holomorphic)
collinear limit. The collinear limit at leading order gives the singular term
of the celestial OPE. We compute the first subleading correction to the OPE by
analysing the four graviton scattering amplitude directly in Mellin space. The
subleading term can be written as a linear combination of BMS descendants with
the OPE coefficients determined by BMS algebra and the coefficient of the
leading term in the OPE. This can be done by defining a suitable BMS primary
state. We find that among the descendants, which appear at the first subleading
order, there is one which is created by holomorphic supertranslation with
simple pole on the celestial sphere.
