Near normal sequences of new lengths n = 4m + 1 = 49,53,57 are constructed. The relation between a special set of near normal sequences and Golay sequences is discussed. A reformulation of Yang's powerful theorems on T-sequences is also given. We give base sequences for lengths m + p, m + p, m, m for p = 1 and m є {19, ... ,30}. Some of these are new lengths, or new decompositions into four squares for n and constructed here for the first time.