We recall that a differentiation basis \({\mathcal A}\) is a collection of open bounded sets in \(\mathbb{R}^n\) such that for each \(x\in\mathbb{R}^n\) there is a sequence \(\{A_j\}\subset{\mathcal A}\) with \(x\in A_j\) for every \(j\) and diameter of \(A_j\) tending to \(0\) as \(j\to\infty\). A differentiation basis \({\mathcal A}\) is said to differentiate the integral of a locally integrable function \(f\) defined in \(\mathbb{R}^n\) if the limit relation \[ {1\over| A|} \int_A f(y)\,dy\to f(x)\quad\text{as}\quad \text{diam}(A)\to 0,\;x\in A\in{\mathcal A} \] holds for almost every \(x\in \mathbb{R}^n\), where \(| A|\) is the Lebesgue measure of the set \(A\). If \({\mathcal A}\) differentiates the integral of every function of a given class, one says that \({\mathcal A}\) differentiates that class. The authors consider the basis \({\mathcal B}\) of all arbitrarily oriented rectangular parallelepipeds in \(\mathbb{R}^n\) with diameter less than 1. They prove that (i) \({\mathcal B}\) differentiates the Besov space \(B^{\alpha,1}_p(\mathbb{R}^n)\) if \(1\leq p 1\).