This paper reveals a mysterious law governing the Doppler effect of light. A new exponential term is introduced: eV/c . Einstein's thought experiment ( chasing a beam of light ) is very compelling and can be considered as self-evident. It is an immediate consequence of the non-existence of light carrying medium ( ether). The speed of light should be constant c independent not only of source velocity, but also of observer velocity. However, Einstein made a serious mistake when he tried to explain this. He misinterpreted the constancy of the speed of light as the relativity of space and time. This is an extraordinary, farfetched claim. Therefore, relativistic Doppler effect formula is based on a wrong foundation. Moreover, all existing theories of light ( special relativity, ether theory, emission theory) fail to explain Doppler effect for source- observer relative velocities greater than the speed of light. Although special relativity imposes that no ( relative ) velocity is greater than the speed of light, it is easy to obtain relative velocities greater than the speed of light without violating the universal speed limit. This can be done by an arrangement consisting of light source, observer and a mirror. Suppose that a light source and an observer are at rest relative to each other and located close to each other. Light emitted by the source goes to a distant mirror and is reflected back to the observer, while the mirror is moving towards the source and observer with velocity close to the speed of light. In this case, the velocity of the mirror image of the source relative to the observer is equal to 2c, for which the relativistic Doppler effect formula will be undefined because β = V/c will be greater than 1, resulting in a square root of a negative number. Theoretically, it is possible to get unlimited relative velocity between the mirror image of the source and the observer by using multiple moving mirrors. Therefore, a new theory of the real law governing the Doppler effect of light is required. Einstein's thought experiment can be understood as the constancy of phase velocity, not group velocity. The phase velocity of light is always constant c irrespective of source and observer motion. The group velocity of light behaves in a more conventional way: it is independent of source velocity, but dependent on observer velocity. The constancy of the phase velocity requires, unconventionally, not only change in frequency, but also change in wavelength for a moving observer. Even though this is also counter intuitive, it is not as farfetched as 'length contraction and time dilation'. Therefore, λ . f = λ’. f ’ = c . This theory invokes another problem: then what is the law governing the Doppler effect of light. The new law of Doppler effect of light is proposed as: f ‘ = f . e V/ c , λ’ = λ . e -V/ c , where V is positive for source and observer approaching each other. This theory explains the Ives-Stilwell experiment.