  The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl,
41 (2020), 1797--1825]. In that work, an approximation procedure was proposed
for orthogonal low-rank tensor approximation; however, the approximation lower
bound was only established when the number of orthonormal factors is one. To
this end, by further exploring the multilinearity and orthogonality of the
problem, we introduce a modified approximation algorithm. Approximation lower
bound is established, either in deterministic or expected sense, no matter how
many orthonormal factors there are. In addition, a major feature of the new
algorithm is its flexibility to allow either deterministic or randomized
procedures to solve a key step of each latent orthonormal factor involved in
the algorithm. This feature can reduce the computation of large SVDs, making
the algorithm more efficient. Some numerical studies are provided to validate
the usefulness of the proposed algorithm.
