  We study the convergence of the Laurent polynomials of Lagrange interpolation
on the unit circle for continuous functions satisfying a condition about their
modulus of continuity. The novelty of the result is that now the nodal systems
are more general than those constituted by the n roots of complex unimodular
numbers and the class of functions is different from the usually studied.
Moreover, some consequences for the Lagrange interpolation on [-1,1] and the
Lagrange trigonometric interpolation are obtained.
