In order to show a potential power of a negative muon spin rotation and relaxation (mu-SR) technique for observing local magnetic environments, we here want to propose a mu-SR experiment on MgB2. Here, negative muons are trapped by either Mg or B. The negative muons trapped by B will provide no mu-SR signal due to nuclear magnetic moment of B, while the muons trapped by Mg will do a clear mu-SR signal formed by nuclear magnetic moments of B. Therefore, we will see a local magnetic field from the Mg site. This has a significant advantage over the positive muon spin rotation and relaxation (mu+SR) technique, because positive muons are known to diffuse in MgB2 even at temperatures above 12.5 K. As a result, it is very difficult to study a dynamic behavior of the internal magnetic field, particularly at around the superconducting transition temperature (39 K).