A class of communication tasks, called isotropic, was introduced in [15], and minimum completion time algorithms for all tasks in this class were found. Isotropic tasks are characterized by a type of symmetry with respect to origin node. In this paper we consider the problem of transposing a sparse matrix of size N N with a diagonal band of size 2 β + 1 + 1, which is stored by columns in a hypercube network of N=2 d processors. We propose an assignment of matrix columns to hypercube nodes such that the transposition becomes a nearly isotropic task, that is, it looks almost identical to all nodes. Under this assignment, we give an algorithm to transpose the matrix in 2 β steps. We prove that the algorithm given is optimal over all affine assignments of columns to processors. We also derive a lower bound on the minimum number of steps required to transpose a banded matrix, which holds for any possible assignment of matrix columns to hypercube processors. In the case that 2 β + 1 + 1=Θ(N c ), for some constant c (0, 1], we prove that the completion time of our transposition algorithm is of the same order of magnitude with the lower bound. We further show that d/β banded matrices, each of bandwidth 2 β + 1 + 1, can be stored by columns in a hypercube so that all of them can be concurrently transposed in 2 β + 1 steps. Finally, we modify our algorithms so that they apply to arbitrary matrix bandwidths and multiple column storage by each processor, while maintaining their efficiency.