  High temperature superconductivity is often found in the vicinity of
antiferromagnetism. This is also true in LaFeAsO$_{1-x}$F$_{x}$ ($x \leq$ 0.2)
and many other iron-based superconductors, which leads to proposals that
superconductivity is mediated by fluctuations associated with the nearby
magnetism. Here we report the discovery of a new superconductivity dome without
low-energy magnetic fluctuations in LaFeAsO$_{1-x}$F$_{x}$ with 0.25$\leq x
\leq$0.75, where the maximal critical temperature $T_c$ at $x_{opt}$ =
0.5$\sim$0.55 is even higher than that at $x \leq$ 0.2. By nuclear magnetic
resonance and Transmission Electron Microscopy, we show that a C4 rotation
symmetry-breaking structural transition takes place for $x>$ 0.5 above $T_c$.
Our results point to a new paradigm of high temperature superconductivity.
