  We study surfaces with parallel normalized mean curvature vector field in
Euclidean or Minkowski 4-space. On any such surface we introduce special
isothermal parameters (canonical parameters) and describe these surfaces in
terms of three invariant functions.
  We prove that any surface with parallel normalized mean curvature vector
field parametrized by canonical parameters is determined uniquely up to a
motion in Euclidean (or Minkowski) space by the three invariant functions
satisfying a system of three partial differential equations. We find examples
of surfaces with parallel normalized mean curvature vector field and solutions
to the corresponding systems of PDEs in Euclidean or Minkowski space in the
class of the meridian surfaces.
