  Unlike the Lorentz transformation which replaces the Galilean transformation
among inertial frames at high relative velocities, there seems to be no such a
consensus in the case of coordinate transformation between inertial frames and
uniformly rotating ones. There have been some attempts to generalize the
Galilean rotational transformation to high rotational velocities. Here we
introduce a modified version of one of these transformations proposed by Philip
Franklin in 1922. The modified version is shown to resolve some of the
drawbacks of the Franklin transformation, specially with respect to the
corresponding spacetime metric in the rotating frame. This new transformation
introduces non-inertial eccentric observers on a uniformly rotating disk and
the corresponding metric in the rotating frame is shown to be consistent with
the one obtained through Galilean rotational transformation for points close to
the rotation axis. Employing the threading formulation of spacetime
decomposition, spatial distances and time intervals in the spacetime metric of
a rotating observer's frame are also discussed.
