  In this note, we provide analytic expressions for the R\'enyi common
information of orders in $(1,\infty)$ for the doubly symmetric binary source
(DSBS). Until now, analytic expressions for the R\'enyi common information of
all orders in $[0,\infty]$ have been completely known for this source. We also
consider the R\'enyi common information of all orders in $[-\infty,0)$ and
evaluate it for the DSBS. We provide a sufficient condition under which the
R\'enyi common information of such orders coincides with Wyner's common
information for the DSBS. Based on numerical analysis, we conjecture that there
is a certain phase transition as the crossover probability increasing for the
R\'enyi common information of negative orders for the DSBS. Our proofs are
based on a lemma on splitting of the entropy and the analytic expression of
relaxed Wyner's common information.
