  In this paper, we study the blow-up of a sequence of Yang-Mills connection
with bounded energy on a four manifold. We prove a set of equations relating
the geometry of the bubble connection at the infinity with the geometry of the
limit connection at the energy concentration point. These equations exclude
certain scenarios from happening, for example, there is no sequence of
Yang-Mills $SU(2)$ connections on $S^4$ converging to an ASD one-instanton
while developing a SD one-instanton as a bubble. The proof involves the
expansion of connection forms with respect to some Coulomb gauge on long
cylinders.
