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Using a simple tight-binding model and the Kubo formula we have calculated the lateral distribution of the tunneling conductance across a magnetic tunnel junction probed by STM. We find that the presence of an isolated impurity within the barrier layer can cause a spike in the conductance distribution, which is in agreement with recent experiments. We show that the local tunneling magnetoresistance (TMR) is very sensitive to the electronic state of the impurity and to the lateral position of the tip. The latter dramatic variation in TMR could be detected by STM.