This study describes a new chemometric tool for the identification of relevant volatile compounds in cork by untargeted headspace solid phase microextraction and gas chromatography mass spectrometry (HS-SPME/GC-MS) analysis. The production process in cork industries commonly includes a washing procedure based on water and temperature cycles in order to reduce off-flavors and decrease the amount of trichloroanisole (TCA) in cork samples. The treatment has been demonstrated to be effective for the designed purpose, but chemical changes in the volatile fraction of the cork sample are produced, which need to be further investigated through the chemometric examination of data obtained from the headspace. Ordinary principal component analysis (PCA) based on the numerical description provided by the chromatographic area of several target compounds was inconclusive. This led us to consider a new tool, which is presented here for the first time for an application in the chromatographic field. The superposing significant interaction rules (SSIR) method is a variable selector which directly analyses the raw internal data coming from the spectrophotometer software and, combined with PCA and discriminant analysis, has been able to separate a group of 56 cork samples into two groups: treated and non-treated. This procedure revealed the presence of two compounds, furfural and 5-methylfurfural, which are increased in the case of treated samples. These compounds explain the sweet notes found in the sensory evaluation of the treated corks. The model that is obtained is robust; the overall sensitivity and specificity are 96% and 100%, respectively. Furthermore, a leave-one-out cross-validation calculation revealed that all of the samples can be correctly classified one at a time if three or more PCA descriptors are considered.