  We study the minimal free resolution of the tangent cone of Gorenstein
monomial curves in affine 4-space. We give the explicit minimal free resolution
of the tangent cone of non-complete intersection Gorenstein monomial curve
whose tangent cone has five minimal generators and show that the possible Betti
sequences are $(1,5,6,2)$ and $(1,5,5,1)$. Also, we compute the Hilbert
function of the tangent cone of these families as a result.
