This paper describes and experimentally evaluates a new variation of multiclass classification using support vector machines. The technique, called pairwise adaptive support vector machines (pa-SVM), is a one-vs-one multiclass classifier with each binary classifier optimized towards using the best (C,γ) parameter pair to obtain the best correct classification rate. An exponential grid search and a 10-fold cross validation algorithm was used to determine the best (C,γ) pair. To evaluate multiple (C,γ) pairs for each binary classifier with the same best correct classification rate, four scenarios of C and γ were explored (min C min γ, min C max γ, max C min γ and max C max γ). Each experiment used the radial basis function (RBF) kernel for training, and the results were obtained on 23 real world datasets from the UCI Machine Learning Repository. The results show that the pa-SVM approach mostly outperforms the standard approach and by selecting the max C min γ scenario the number of support vectors is minimized. Furthermore, the comparison of our results with recent studies using the same datasets show that the new technique is very competitive.