  The seminal work \cite{bm} by Brezis and Merle has been pioneering in
studying the bubbling phenomena of the mean field equation with singular
sources. When the vortex points are not collapsing, the mean field equation
possesses the property of the so-called "bubbling implies mass concentration".
Recently, Lin and Tarantello in \cite{lt} pointed out that the "bubbling
implies mass concentration" phenomena might not hold in general if the collapse
of singularities occurs. In this paper, we shall construct the first concrete
example of non-concentrated bubbling solution of the mean field equation with
collapsing singularities.
