In this contribution we propose an efficient method for computing symbol-based extrinsic information transfer (EXIT) charts, which are useful for estimating the convergence properties of non-binary iterative decoding. A standard solution is to apply a priori reliability information to the a posteriori probability (APP) constituent decoder and compute the resultant average extrinsic information at the decoder's output using multidimensional histogram measurements. However, the employment of this technique is only feasible for a low number of bits per symbol, since the complexity of this approach increases exponentially with the number of bits per symbol. We demonstrate that by averaging over a function of the extrinsic APPs for a long block the extrinsic information can be estimated at a low complexity. In contrast to using histogram measurements, the proposed technique allows us to generate EXIT charts even for a high number of bits per symbol. Our design examples using either a non-binary serial concatenated code or turbo trellis-coded modulation demonstrate the attractive benefits of the proposed approach.