The invention provides a catheter for ice mapping and ablation and a method of ablation using the catheter. The catheter includes at least two conduits for circulating a refrigerating fluid adjacent an ablation device located at the end of a catheter. The refrigerated ablation device is used to chill a localized region of myocardial tissue, thereby permitting the resulting change in electrical activity to be determined. In response to the test results, the ablation device may be used to make a lesion in the myocardial tissue to correct a cardiac arrhythmia. In one embodiment, the ablation device is an electrode which uses radio frequency energy to ablate the myocardial tissue. Alternatively, the ablation device is an electrode adapted for direct current ablation. In another embodiment, the electrode is replaced with an optical fiber in communication with a laser which uses the laser's light energy to ablate tissue. Yet another embodiment is a cryogenic catheter having combined or separate mapping and ablation devices. In another embodiment, a cryogenic catheter is provided having an inner conduit with a stepped down diameter. The embodiments may include provisions for steering the catheter and for stabilizing the ablation device at the proposed lesion site.