Gelus's Death Note

"This is the notebook that caused Gelus to die when he saved Misa. It would pass from Rem to Misa and eventually Mikami. This is the notebook that played the key role in the battle with Near."

- Death Note 13: How to Read

Gelus's Death Note is the second Death Note used in the series and is primarily owned by Misa Amane after Gelus dies. She relinquishes ownership twice: once on Rem's suggestion during her detainment by the Japanese Task Force, during which Ryuk becomes the Shinigami tied to the notebook, and again on Light Yagami's orders after the timeskip. The notebook is later given to Teru Mikami, who operates as Kira while Light is unable to move. It is eventually acquired by the SPK and burned by Near.

Appearance
Gelus's notebook is black with "arvc-5" written in white on the front. The inside of the notebook contains white, ruled pages and it looks like a really old notebook.

Plot
Gelus, a Shinigami, fell in love with Misa Amane and used his Death Note to kill the man who was destined to kill her. Gelus died as a result, leaving only his Death Note behind. The notebook was repossessed by Rem, who took it to the human world and gave it to Misa, whom Rem believed was supposed to have it.

When Misa is detained by the Task Force on suspicion of being the second Kira, she gives up ownership of the notebook to Light, losing her memories of using it and the circumstances of meeting Light in the process. Light has Ryuk and Rem possess each other's Death Notes, so Ryuk is tied to this notebook for the remainder of the series.

While Misa is in confinement, Light buries the notebook in a forest. After he and Misa have been released, he sends Misa to retrieve the notebook, regain possession of it as well as her memories of using it, and instructs her to make the eye deal with Ryuk. Misa uses this notebook for the next five years, killing criminals on Light's orders.

After the timeskip, Light Yagami has Misa relinquish ownership of the notebook with the promise that he wants her to be a normal wife. He sends it to Teru Mikami, who makes the eye deal with Ryuk and acts as Kira while Light is under suspicion from both the SPK and members of his own Task Force. Later, Mikami sends pages of the notebook to Kiyomi Takada and keeps the notebook in a safety deposit box at his bank. He takes sends the names of faces of criminals to Takada while he publicly uses a fake notebook in order to alert the suspicion of his tail. However, the real notebook is discovered and confiscated by Stephen Gevanni and is eventually burned by Near, after which it disappears from the human world.

Trivia

 * The writing on the front, ARVC-5, is in reference to the inherited gene Arrhythmogenic Right Ventricular Cardiomyopathy 5, which can cause sudden heart attacks in people with the gene.