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A procedure for correcting systematic biases across multiple variables is presented. This procedure operates in the frequency domain, using the cross-spectrum across variables to correct bias across each frequency band. The proposed approach is termed multivariate frequency bias correction or MFBC. The approach is illustrated using global climate model (GCM) simulations of multiple atmospheric variables, with variables selected based on recommended usage in downscaling applications. Results indicate clear benefits of using MFBC in representing both intra- and inter-variable dependence in corrected simulations. This has important implications in applications which require multiple atmospheric variables, and a need to correctly simulate both inter- and intra-variable dependence attributes. MFBC offers a mean to correct raw GCM atmospheric variables prior to downscaling or correct dynamically or statistically downscaled simulations prior to derived simulations of other variables of interest. Use of MFBC can have significant implications on derived hydrologic simulations, such as in sizing of storage reservoirs, or devising water sharing plans for the future.