  The normal sequences NS(n) and near-normal sequences NN(n) play an important
role in the construction of orthogonal designs and Hadamard matrices. They can
be identified with certain base sequences (A;B;C;D), where A and B have length
n+1 and C and D length n. C.H. Yang conjectured that near-normal sequences
exist for all even n. While this has been confirmed for n not exceeding 30, so
far nothing else was known for larger n. We show that NN(32) consists of 8
equivalence classes and we exhibit their representatives. We also construct
representatives for two equivalence classes of NN(34). On the other hand our
exhaustive computer searches show that NS(31) and NS(33) are void.
