In 1998, the Certified Public Accountant of Republic of China (ROCCPA), in response to a request by the Federal Trade Commission (FTC), abolished the audit fee floor in Taiwan. Past literature has pointed out that the audit market would become more competitive, and accounting firms with brand name reputation would get more market share after abolishing the audit fee floor. In this paper, we investigate the association between the abolishment of audit fee floor and audit quality. We also examine the effects of brand name reputation and auditor switch on such association. We discovered that the overall audit quality has increased after abolishing the audit fee floor, a conclusion that supports the original decision of abolishment. We also found that the audit quality of accounting firms with brand name reputation increased less than that of non-brand name accounting firms. This demonstrates that improving audit quality alone does not lead to a bigger market share, and a non-brand name firm cannot become a brand-name firm solely by increasing audit quality.