  Following Burstall and Hertrich-Jeromin we study the Ribaucour transformation
of Legendre submanifolds in Lie sphere geometry. We give an explicit
parametrization of the resulted Legendre submanifold $\hat{F}$ of a Ribaucour
transformation, via a single real function $\tau$ which represents the regular
Ribaucour sphere congruence $s$ enveloped by the original Legendre submanifold
$F$.
