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This paper investigates the benefits of amplify-and-forward (AF) relaying in the setup of multiantenna wireless networks. For this purpose, random sequential (RS) relaying is studied. It is shown that random unitary matrix multiplication at the relay nodes empowers the RS scheme to achieve a better diversity-multiplexing tradeoff (DMT) as compared to the traditional AF relaying. First, the RS scheme is proved to achieve the optimum DMT for a multiantenna full-duplex single-relay two-hop network. Applying this result, a new achievable DMT is derived for the case of multiantenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multiantenna two parallel noninterfering half-duplex relays. Furthermore, random unitary matrix multiplication is shown to also improve the DMT of the nonorthogonal AF relaying scheme for the case of a multiantenna single relay channel. Finally, the general case of multiantenna full-duplex relay networks is studied. First, a new lower-bound is derived on its DMT using the RS scheme. Furthermore, maximum multiplexing gain of the network is also shown to be achievable by traditional amplify-forward relaying. The gain value is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes.