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The spin splitting of the exciton states in semiconductor asymmetrical coupled quantum dots (CQDs) containing a single magnetic ion is theoretically investigated.It is found that the spin splitting is not the largest when the electric field is zero.An electric field stronger than that in symmetrical CQDs is necessary to switch the splitting on/off.The mixing between the bonding and antibonding hole states consequently results in the bright-to-dark transition of the ground exciton in the photoluminescence spectrum.