Let \(F\) be a local field of characteristic 0 and \(\pi\) an infinite- dimensional irreducible admissible representation of \(GL(2,F)\). For any quadratic extension \(L\) of \(F\), Tunnell gave an expression for the restriction of the character of \(\pi\) to \(L^*\subset GL(2,F)\) as a sum of characters of \(L^*\) with coefficients expressed in terms of the \(\varepsilon\)-factors of the base change lift of \(\pi\) to \(GL(2,L)\). That sum was explicitly computed by Tunnell and the results case by case compared with existing character tables. Now the author gives a more natural proof of Tunnell’s formula: he computes the twisted character of the base change lift of \(\pi\) directly in terms of \(\varepsilon\)-factors. This gives the result, without restriction on the residual characteristic.