Don’t worry if you need a symmetric power supply and you don’t have a center tapped transformer. The circuit below solve your problem. You can see the second bridge diode is powered via capacitor decoupling, so it’s DC isolated. Because it’s DC isolated, we can connect the ground together to form a symmetric supply.

symmetric supply circuit schematic

Because the second rectifier is powered via capacitors, it suffer a higher impedance than the first rectifier diodes. To minimize the effect, we have to choose the capacitors two times bigger to suppress the ripple voltage on its output.