Iterative Gaussianization (IG) is a versatile technique that transforms multivariate input data into a set of independent Gaussian factors by sequentially applying univariate marginal Gaussianization followed by an orthogonal transformation. The latter relies on techniques such as principal component analysis (PCA) or independent component analysis (ICA) which may become computationally expensive or difficult to scale when applied to high-dimensional data. Recent developments in IG have focused on addressing the curse of dimensionality by employing convolutional rotations to obtain the orthogonal transformations. This paper proposes an alternative approach based on Householder transformations to derive the orthogonal transformations required by IG. Compared to PCA, ICA, and convolutional rotations, this approach is simpler and allows for faster processing of extremely large input datasets. The paper demonstrates this through a case study that benchmarks projection pursuit multivariate transformation (PPMT), IG, and IG with Householder transformation.