We show, assuming the Strong Exponential Time Hypothesis, that for every ε > 0, approximating undirected unweighted Diameter on n-vertex m-edge graphs within ratio 7/4 − ε requires m^4/3−o(1) time, even when m = Õ(n). This is the first result that conditionally rules out a near-linear time 5/3-approximation for undirected Diameter.