  We revisit the calculation of a heavy quark potential in N =4 supersymmetric
Yang-Mills theory at finite temperature using the AdS/CFT correspondence. As is
widely known, the potential calculated in the pioneering works of Rey et al.
and Brandhuber et al. is zero for separation distances r between the quark and
the anti-quark above a certain critical separation, at which the potential has
a kink. We point out that by analytically continuing the string configurations
into the complex plane, and using a slightly different renormalization
subtraction, one obtains a smooth non-zero (negative definite) potential
without a kink. The obtained potential also has a non-zero imaginary
(absorptive) part for separations r > r_c = 0.870/\pi T . At large separations
r the real part of the potential does not exhibit the exponential Debye falloff
expected from perturbation theory and instead falls off as a power law,
proportional to 1/r^4 for r > r_0 = 2.702 / \pi T.
