NOTATION OF GUARANTEE

Exhibit 4.2

NOTATION OF GUARANTEE

For value received, each Guarantor (which term includes any successor Person under the Indenture) has, jointly and severally, fully and unconditionally and irrevocably guaranteed, to the extent set forth in the Indenture, dated as of April 20, 2006 (the “ Indenture ”), among Brigham Exploration Company, a Delaware corporation (the “ Company ”), the Guarantors and Wells Fargo Bank, N.A., as trustee (the “ Trustee ”), and subject to the provisions in the Indenture, (a) the due and punctual payment of the principal of, premium, if any, and interest on the Notes (as defined in the Indenture), whether at maturity, by acceleration, redemption or otherwise, the due and punctual payment of interest on overdue principal and premium, and, to the extent permitted by law, i