  To solve the discrepancy between the experimental data on the partial widths
and lineshapes of the dipion emission of $\Upsilon(4S)$ and the theoretical
predictions, we suggest that there is an additional contribution which was not
taken into account in previous calculations. Noticing that the mass of
$\Upsilon(4S)$ is above the production threshold of $B\bar B$, the contribution
of the sequential process $\Upsilon(4S)\to B\bar B\to \Upsilon(nS)+S\to
\Upsilon(nS)+\pi^+\pi^-$ ($n=1,2$) may be sizable, and its interference with
that from the direct production would be important. The goal of this work is to
investigate if a sum of the two contributions with a relative phase indeed
reproduces the data. Our numerical results on the partial widths and the
lineshapes $d\Gamma(\Upsilon(4S)\to
\Upsilon(2S,1S)\pi^+\pi^-)/d(m_{\pi^+\pi^-})$ are satisfactorily consistent
with the measurements, thus the role of this mechanism is confirmed. Moreover,
with the parameters obtained by fitting the data of the Belle and Babar
collaborations, we predict the distributions $d\Gamma(\Upsilon(4S)\to
\Upsilon(2S,1S)\pi^+\pi^-)/d\cos\theta$ which have not been measured yet.
