Several studies have shown that in sociophonetic research Lobanov’s speaker normalization method outperforms other methods for normalizing vowel formants of speakers. An ad- vantage of Lobanov’s method compared to the method that was introduced by Watt & Fabricius in 2002 is that it is independent of the shape of the vowel space area, and also normalizes to the dispersion of the vowels. However, it does depend on the distribution of the vowels within the vowel space. When us- ing Lobanov normalization the formant values are converted to z-scores. We present a method where the μ in the z-score for- mula is replaced by the center of the convex hull that encloses the vowels, and the σ is obtained on the basis of the points that constitute the convex hull. When normalizing measurements of two real data sets, and of a series of randomly generated data sets, we found that our method improved in matching vowel spaces in size and overlap.