Given a set of points \(\{(x_i,y_j)\}\) in \(\mathbb R^2\) reordered into an array called square point-grid and a similar square vector-grid composed by vectors associated with the points \((x_i,y_j)\), the authors construct a Thiele-type branched continued fraction defined by two above grids. A numerical example shows that the approximants of this continued fraction called bivariate vector valued rational interpolants still works even if a vector-grid is ill-defined.