This paper addresses design of accelerators using systolic architectures for training of neural networks using a novel gradient interleaving approach. Training the neural network involves backpropagation of error and computation of gradients with respect to the activation functions and weights. It is shown that the gradient with respect to the activation function can be computed using a weight-stationary systolic array while the gradient with respect to the weights can be computed using an output-stationary systolic array. The novelty of the proposed approach lies in interleaving the computations of these two gradients to the same configurable systolic array. This results in reuse of the variables from one computation to the other and eliminates unnecessary memory accesses. The proposed approach leads to 1.4 - 2.2 times savings in terms of number of cycles and $1.9 \times$ savings in terms of memory accesses. Thus, the proposed accelerator reduces latency and energy consumption.