  We explain that, like the usual Pad\'e approximants, the barycentric Pad\'e
approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More
precisely, we show that for every polynomial P there exists a power series S,
with arbitrarily small coefficients, such that the sequence of barycentric
Pad\'e approximants of P + S do not converge uniformly in any subset of the
complex plane with a non-empty interior.
