  The evolution of the Fermi surface of CeRh$_{1-x}$Co$_x$In$_5$ was studied as
a function of Co concentration $x$ via measurements of the de Haas-van Alphen
effect. By measuring the angular dependence of quantum oscillation frequencies,
we identify a Fermi surface sheet with $f$-electron character which undergoes
an abrupt change in topology as $x$ is varied. Surprisingly, this
reconstruction does not occur at the quantum critical concentration $x_c$,
where antiferromagnetism is suppressed to T=0. Instead we establish that this
sudden change occurs well below $x_c$, at the concentration x ~ 0.4 where long
range magnetic order alters its character and superconductivity appears. Across
all concentrations, the cyclotron effective mass of this sheet does not
diverge, suggesting that critical behavior is not exhibited equally on all
parts of the Fermi surface.
