The author finds a pointwise estimate of the remainder of interpolation formula using two multiple nodes from the ends of a closed interval. If \(p\) is the Hermite interpolation polynomial corresponding to a function \(f\in C^{r-1}[-1,1]\), \(r\in\mathbb{N}\), and to the nodes \(-1\) and \(+1\), of order of multiplicity \(r\), then for any \(x\in [-1,1]\) we have the following estimate of the error \[ | f(x)-p(x)|\leq C_ r(1-x^ 2) \omega_{r+1} \left( f^{(r-1)}; {2\over {r+1}} (1-x^ 2)^{(r+1)^{-1}} \right), \] where \(\omega_{r+1}\) is the modulus of smoothness of order \(r+1\), while \(C_ r\) is a positive value depending only on \(r\). For \(r=1\) it reduces to the known inequality \(| f(x)- p(x)|\leq 15\omega_ 2 (f; \sqrt{1-x^ 2})\) of A. F. Timan and L. J. Strukov [The theory of the approximation of functions, Proc. Int. Conf., Collect. Artic. Kaluga 1975, 338-341 (1977; Zbl 0493.41007)].