We report on the demonstration and characterization of a non-volatile graphene-based memory, where the resistance level can be reversibly modulated with a contrast exceeding 400. We study two-terminal devices consisting of highly crystalline (Raman I(D)/I(G) H 0.2) monolayer CVD-graphene micro-ribbons transferred on SiO2 after growth on Cu. Electrical characterizations right after fabrication show the expected Ohmic behavior with k© resistance level and no memory effect. A breakdown technique turns the resistive devices into memories: we apply a voltage sweep up to 30V (a few mA). During the sweep, several moderate jumps in resistance are observed, followed by a final rise to a high resistance state (several M©). As evidenced by Raman mapping, the resulting material is highly disordered graphene (I(D)/I(G) H 1.3) covering the whole device surface. After breakdown, the resistance can be reversibly set at two well-separated levels (e.g. 0.1 M© and 10 M©) by applying low voltage pulses (10V; 1-100 ŒA) in vacuum. Both conductance states feature the Poole-Frenkel conduction mode, as is typical in disordered carbon. No loss of matter or physical gap is observed with either SEM or AFM. Overall, our results suggest that the reversible switching is mostly due to thermally-induced increase or decrease in sp2 grain size in disordered graphene. This is significantly different from the commonly reported switching mechanism based on conducting filaments bridging a physical gap.