We describe a simple but effective way of using multi-frame targets to improve the accuracy of Artificial Neural Network- Hidden Markov Model (ANN-HMM) hybrid systems. In this approach a Deep Neural Network (DNN) is trained to predict the forced-alignment state of multiple frames using a separate softmax unit for each of the frames. This is in contrast to the usual method of training a DNN to predict only the state of the central frame. By itself this is not sufficient to improve accuracy of the system significantly. However, if we average the predic- tions for each frame - from the different contexts it is associated with - we achieve state of the art results on TIMIT using a fully connected Deep Neural Network without convolutional archi- tectures or dropout training. On a 14 hour subset of Wall Street Journal (WSJ) using a context dependent DNN-HMM system it leads to a relative improvement of 6.4%% on the dev set (test- dev93) and 9.3%% on test set (test-eval92).