Edge computing is a promising technology that provides cloud-like computing services at the network edge in close proximity to mobile devices. In this article, we propose a new paradigm of cooperative edge computing that exploits parallel transmission over the whole resource block of NOMA for parallel computation offloading. Specifically, we consider a basic three-node model consisting of a user, a helper, and an AP. The user can simultaneously offload a task to the helper and AP using NOMA, and the helper can compute or/and relay the received task from the user. We first discuss the scenario where the helper acts as either a computing server or a relay. Then we devise a general framework in which the helper has the double roles of assisting the user and has its own task to execute. We show that the proposed scheme can achieve a win-win situation for both the user and helper. Simulations are conducted to illustrate the superior performance of the proposed scheme compared to the conventional schemes without cooperation.