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We study the second moment boundedness of solutions of linear stochastic delay differential equations. First, we give a framework, for general N-dimensional linear stochastic differential equations with a single discrete delay, of calculating the characteristic function for the second moment boundedness. Next, we apply the proposed framework to a special case of a type of 2-dimensional equation that the stochastic terms are decoupled. For the 2-dimensional equation, we obtain the characteristic function explicitly given by equation coe cients, and the characteristic function gives sufficient conditions for the second moment to be bounded or unbounded.