The authors study the linear independence of T-spline blending functions, a property required in the isogeometric analysis. The class of T-splines, for which no perpendicular T-node extensions intersect, is studied and in this purpose, first a technique to construct a matrix that maps a T-spline control point to a control point of an equivalent nonuniform rational B-spline (NURBS) surface is presented and then the full rank condition for this matrix is proved to be equivalent with the linear independence of the blending functions of T-splines.