Finite elements with support on two intervals span the space of piecewise polynomomials with degree 2 n - 1 and n - 1 continuous derivatives. Function values and n - 1 derivatives at each meshpoint determine these `Hermite finite elements'. The n basis functions satisfy a dilation equation with n by n matrix coefficients. Orthogonal to this scaling subspace is a wavelet subspace. It is spanned by the translates of n wavelets Wi(t), each supported on three intervals. The wavelets are orthogonal to all rescalings Wi(2jt-k), but not to translates at the same level (j equals 0). These new multiwavelets achieve 2 n vanishing moments and high regularity with symmetry and short support.