This work shows that a differentiable activation function is not necessary any more for error backpropagation. The derivative of the activation function can be replaced by an iterative temporal differencing using fixed random feedback alignment. Using fixed random synaptic feedback alignment with an iterative temporal differencing is transforming the traditional error backpropagation into a more biologically plausible approach for learning deep neural network architectures. This can be a big step toward the integration of STDP-based error backpropagation in deep learning.