With the rise of attacks on online accounts in the past years, more and more services offer two-factor authentication for their users. Having factors out of two of the three categories something you know, something you have and something you are should ensure that an attacker cannot compromise two of them at once. Thus, an adversary should not be able to maliciously interact with one's account. However, this is only true if one considers a weak adversary. In particular, since most current solutions only authenticate a session and not individual transactions, they are noneffective if one's device is infected with malware. For online banking, the banking industry has long since identified the need for authenticating transactions. However, specifications of such authentication schemes are not public and implementation details vary wildly from bank to bank with most still being unable to protect against malware. In this work, we present a generic approach to tackle the problem of malicious account takeovers, even in the presence of malware. To this end, we define a new paradigm to improve two-factor authentication that involves the concepts of one-out-of-two security and transaction authentication. Web authentication schemes following this paradigm can protect security-critical transactions against manipulation, even if one of the factors is completely compromised. Analyzing existing authentication schemes, we find that they do not realize one-out-of-two security. We give a blueprint of how to design secure web authentication schemes in general. Based on this blueprint we propose FIDO2 With Two Displays (FIDO2D), a new web authentication scheme based on the FIDO2 standard and prove its security using Tamarin. We hope that our work inspires a new wave of more secure web authentication schemes, which protect security-critical transactions even against attacks with malware.