  We obtain supremum of the k-th normalized Steklov eigenvalues of all
rotational symmetric conformal metrics on the cylinder with k>1. The case k=1
for all conformal metrics has been completely solved by Fraser and Schoen. We
give geometric description in terms of minimal surfaces for metrics attaining
the supremum. We also obtain some partial results on the comparison of the
normalized Stekov eigenvalues of rotationally symmetric metrics and general
conformal metrics on the cylinder. A counter example is constructed to show
that for that the first normalized Steklov eigenvalue of rotationally symmetric
metric may not be larger.
