Machine learning models have shown exceptional prowess in solving complex issues across various domains. However, these models can sometimes exhibit biased decision-making, resulting in unequal treatment of different groups. Despite substantial research on counterfactual fairness, methods to reduce the impact of multivariate and continuous sensitive variables on decision-making outcomes are still underdeveloped. We propose a novel data pre-processing algorithm, Orthogonal to Bias (OB), which is designed to eliminate the influence of a group of continuous sensitive variables, thus promoting counterfactual fairness in machine learning applications. Our approach, based on the assumption of a jointly normal distribution within a structural causal model (SCM), demonstrates that counterfactual fairness can be achieved by ensuring the data is orthogonal to the observed sensitive variables. The OB algorithm is model-agnostic, making it applicable to a wide range of machine learning models and tasks. Additionally, it includes a sparse variant to improve numerical stability through regularization. Empirical evaluations on both simulated and real-world datasets, encompassing settings with both discrete and continuous sensitive variables, show that our methodology effectively promotes fairer outcomes without compromising accuracy.