In the recent paper \u201cOn certain Vandermonde determinants whose variables separate\u201d [Linear Algebra
and its Applications 449 (2014) pp. 17\u201327], there was established a factorized formula for some
bivariate Vandermonde determinants (associated to almost square grids) whose basis functions are
formed by Hadamard products of some univariate polynomials. That formula was crucial for proving
a conjecture on the Vandermonde determinant associated to Padua-like points. In this note we show
that the same formula holds when those polynomials are replaced by arbitrary functions and we
extend this formula to general rectangular grids. We also show that the Vandermonde determinants
associated to Padua-like points are nonvanishing
