Non-native English writers often make preposition errors in English language. The most commonly occurring preposition errors are preposition replacement, preposition missing and unwanted preposition. So, in this method, a system is developed for finding and handling the English preposition errors in preposition replacement case. The proposed method applies 2-Singular Value Decomposition (SVD²) concept for data decomposition resulting in fast calculation and these features are given for classification using Support Vector Machines (SVM) classifier which obtains an overall accuracy above 90%. Features are retrieved using novel SVD² based method applied on trigrams which is having a preposition in the middle of the context. A matrix with the left and right vectors of each word in the trigram is computed for applying SVD² concept and these features are used for supervised classification. Preliminary results show that this novel feature extraction and dimensionality reduction method is the appropriate method for handling preposition errors.