no he didnt betrey him
he just messed up and ruined it of lighto

he widrew the real notebook instead of the fake on and he didnt knew he was being followed and they switched the notebook and also the got the ability to see the shinigami that followed him around and were able to checkmate light in the end =/
his partner that was with him suicided in jail 10 later (planned out by near)
notebook they said near had burned away but that what they just say he could have kept it

there realy long huge story to it and i dont feel like that i want explain it