Impertinence

Impertinence (見当違い, Kentō chigai) is the fourth chapter of volume six and forty-seventh chapter of the Death Note manga series.

Plot
Misa Amane has been touched by a piece of paper from the Death Note and she can now see Rem the Shinigami who is holding her tightly in the ladies' room of the Yotsuba building.

Rem knows that touching Misa with the piece of paper will not restore her memories of being the Second Kira—for that she will have to touch an actual Death Note book. However, she proceeds to tell Misa to stay calm since she is on her side.

Meanwhile, at the Kira Task Force HQ, Light Yagami is examining the details of the recent Kira killings and has made an interesting discovery. The original Kira only killed hardened criminals and people who killed with malice. The current Kira however has a very different approach: He is killing just about anyone reported on the news as having killed whatever the circumstances. For example, Kira recently killed the driver of a car who had run over and killed a pedestrian! Anyone could tell that it was an accident and the original Kira would not have bothered. He was also known to spare killers if he thought that their victims actually deserved to die.

Light is a little troubled at the fact that the original Kira's ideals are remarkably similar to his own and has to remind himself that he is not Kira. On the other hand, he is sure that L has also noticed the different patterns but has not raised them. Could it be because L still suspects Light of being Kira?

Meanwhile in the ladies' room at the Yotsuba building, Rem tells Misa that Light was Kira and tells her all about the Death Note and how Light used it to kill criminals! Misa is excited at the idea that the man she loves is also Kira!

Rem also tells Misa about how she was the Second Kira and was even more powerful than the original since she had the Shinigami Eyes. Misa realizes that L was right all along about her and Light even though he could not prove it.

Rem asks Misa what Light is up to at the moment and she confirms that he and L have joined forces in the search for Kira, to the point that they are even handcuffed together.

Slowly but surely, Misa begins to understand what happened and how she and then Light lost all memories of being Kiras. She even asks Rem to restore her abilities in order to help Light but the Shinigami refuses since Misa has already given up half her life for the Shinigami Eyes and even almost died for Light. The fact that she went so far for him actually delights Misa!

Rem once disliked Light Yagami but having seen the corrupt and self-serving nature of the Yotsuba Kira now believes that his desire to purify the world by killing criminals was probably a more noble undertaking than she originally thought. That being the case, however, killing L and anyone else who gets in Light's way, may cause her own death by extending the lifespan of a human she cares for.

Rem is telling Misa all of this because she knows that the Yotsuba Kira will eventually kill Misa. However, she also warns Misa not to tell Light anything that she has learned. His whole plan hinges on clearing his name and for him to find out about his forgotten past before he is ready could be disastrous. It is therefore up to him to recover the Death Note and hence his memories.

The Shinigami rules prevent Rem from telling Misa who the current Kira is but she indicates that she will drop a hint the moment Misa returns to the interview with the Yotsuba executives. She warns her not to trust the current Kira and is prepared to kill both him and Light should anything happen to Misa.

Before leaving, Rem reminds Misa not tell Light anything in case L finds out about it and thus ruins Light's plan. Misa is equally excited to learn that she even outsmarted Light by finding out he was Kira before he had learned that she was the Second Kira. Rem leaves.

Misa returns to the room where she was being interviewed. The interviewers are waiting for her and she can see Rem standing behind one of them. She now knows who is Kira!

Conception
Ohba said the chapter's title "Impertinence" is for when Rem reveals some secrets early to Misa. This is when Rem knows that Light has a plan, and she tells Misa which Yotsuba member has the Death Note.