Multioutput　regression,　referring　to　simultaneously　predicting　multiple　continuous　output　variables　with　a　single　model,　has　drawn　increasing　attention　in　the　machine　learning　community　due　to　its　strong　ability　to　capture　the　correlations　among　multioutput　variables.　The　methodology　of　output　space　embedding,　built　upon　the　low-rank　assumption,　is　now　the　mainstream　for　multioutput　regression　since　it　can　effectively　reduce　the　parameter　numbers　while　achieving　effective　performance.　The　existing　low-rank　methods,　however,　are　sensitive　to　the　noises　of　both　inputs　and　outputs,　referring　to　the　noise　problem.　In　this　article,　we　develop　a　novel　multioutput　regression　method　by　simultaneously　alleviating　input　and　output　noises,　namely,　robust　multioutput　regression　by　alleviating　input　and　output　noises　(RMoR-Aion),　where　both　the　noises　of　the　input　and　output　are　exploited　by　leveraging　auxiliary　matrices.　Furthermore,　we　propose　a　prediction　output　manifold　constraint　with　the　correlation　information　regarding　the　output　variables　to　further　reduce　the　adversarial　effects　of　the　noise.　Our　empirical　studies　demonstrate　the　effectiveness　of　RMoR-Aion　compared　with　the　state-of-the-art　baseline　methods,　and　RMoR-Aion　is　more　stable　in　the　settings　with　artificial　noise.