ALLONGE TO COMMON STOCK PURCHASE WARRANT (Warrant No. NS2007-1)

Exhibit 4.5

ALLONGE TO COMMON STOCK PURCHASE WARRANT

(Warrant No. NS2007-1)

This Allonge dated and entered into this 30^th day of May, 2007 to the Common Stock Purchase Warrant, Warrant No. NS2007-1, to Purchase 2,125,000 Shares of Common Stock of Transmeridian Exploration Incorporated (the “Warrant”) is made by Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”) for the benefit of North Sound Legacy Institutional Fund LLC, the current holder of the Warrant, for itself and its registered assigns (the “Holder”).

WHEREAS, on May 30, 2007, the Holder pre-paid (the “Prepayment”) the Company $1.99 of the Current Warrant Price of $2.00 per share for 500,000 shares of Warrant Stock (the “Prepayment Warrant Stock”), the receipt of which the Company desires to acknowledge; and

WHEREAS, in order to evidence receipt of the Prepayment and the effect thereof on the Current Warrant Price applicable to the Prepayment Warrant Stock, the Company desires to acknowledge the decrease in the Current Warrant Price applicable to the Prepayment Warrant Stock from $2.00 to $0.01 per share, while leaving all other terms of the Warrant unaffected thereby.

NOW, THEREFORE, for good and valuable consideration (including the Prepayment) and intending to be legally bound hereby, the Company agrees as follows:

IN WITNESS WHEREOF, Transmeridian Exploration Incorporated has caused this Allonge to Common Stock Purchase Warrant to be executed by its duly authorized officer and attested by its Secretary.

Dated: May 30, 2007