If you need +-15 Volts supply and you have only a standard 12V AC transformer, don’t be hurry to buy a new one with center tap, you can use your old transformer! The schematic diagram of this circuit is shown in the figure below.

simmetric double voltage circuit schematic

The voltage before entering the regulator IC 7815 and 7915 might reach 24 volts, if there is no current drawn by load.  The recommended 7815 and 7915 is the IC from Motorola, since they designed for up to 30 Volts input voltage.