In this paper we investigate the polynomial extension technique, which has been used as an alternative to symmetric extension when dealing with orthogonal (non linear-phase) filter banks, since it does not introduce artificial discontinuities either; the drawback of symmetric extension is that it has been traditionally implemented as an expansionist transform. Considering a tree-structured paraunitary FIR filter bank with a minimum number of vanishing moments, we show that polynomial extension leads to a non expansionist invertible subband transform for finite signals. Hence, there is no need of extra samples of the subband signals to achieve perfect reconstruction. Additional advantages of the proposed extension method are also illustrated in our experimental results.