Since Bane introduced the Rule of 2, the Sith sometimes took their late master's lightsaber with them.
Is it possible that count Dooku/Darth Tyranus received Darth Bane's lightsaber, since they are both curved lightsabers?
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This is from the Wookieepedia:
When Dooku became a Jedi Master, he constructed a more personalized lightsaber that had a curved hilt that allowed for precise movements and was designed for a Makashi duelist. It could be shortened with the press of a button, allowing for more flexibility in lightsaber-to-lightsaber combat. This lightsaber had a blue blade, and Dooku wielded it during the Battle of Galidraan. Dooku also occasionally carried a more conventional lightsaber as a Jedi Master.
Possible but unlikely. As the person above me has stated Dooku already saw the advantages of a curved hilt as a Jedi. It is still possible that sidious, after reckognizing his apprentices' affinity to them he passed down Banes Lightsaber. (it's often said that Sidious had dozens of secret locations that he kept for artifacts and special items even before the great purge.