Function approximation using Haar basis systems offers an efficient implementation when compressed via Patricia trees while retaining the flexibility of wavelets for both global and local fitting. However, like B-spline-based approximations, achieving high accuracy in high dimensions remains challenging. This paper proposes KAN/H, a variant of the Kolmogorov-Arnold Network (KAN) that uses a Haar-like hierarchical basis system with nonzero first-order derivatives, instead of B-splines. We also propose a learning-rate scheduling method and a method for handling unbounded real-valued inputs, leveraging properties of linear approximation with Haar-like hierarchical bases. By applying the resulting algorithm to function-approximation problems and MNIST, we confirm that our approach requires minimal problem-specific hyperparameter tuning.