  Distributed Space-Time Block Codes (DSTBCs) from Complex Orthogonal Designs
(CODs) (both square and non-square CODs other than the Alamouti design) are
known to lose their single-symbol ML decodable (SSD) property when used in
two-hop wireless relay networks using amplify and forward protocol. For such a
network, in this paper, a new class of high rate, training-embedded (TE) SSD
DSTBCs are constructed from TE-CODs. The proposed codes include the training
symbols in the structure of the code which is shown to be the key point to
obtain high rate as well as the SSD property. TE-CODs are shown to offer
full-diversity for arbitrary complex constellations. Non-square TE-CODs are
shown to provide higher rates (in symbols per channel use) compared to the
known SSD DSTBCs for relay networks with number of relays less than $10.$
