We propose an efficient method of finding an optimal solution for a multi-item continuous review inventory model in which a bivariate Gaussian probability distribution represents a correlation between the demands of different items. By utilizing appropriate normalizations of the demands, we show that the normalized demands are uncorrelated. Furthermore, the set of equations coupled with different items can be decoupled in such a way that the order quantity and reorder point for each item can be evaluated independently from those of the other. As a result, in contrast to conventional methods, the solution procedure for the proposed method can be much simpler and more accurate without any approximation. To demonstrate the advantage of the proposed method, we present a solution scheme for a multi-item continuous review inventory model in which the demand of optional components depend on that of a "vanilla box", representing the customer's stochastic demand, under stochastic payment and budget constraints. We also perform a sensitivity analysis to investigate the dependence of order quantities and reorder points on the correlation coefficient.