Using a model for the bundle 16e6475c2e261b12e"> of semi-holonomic second order frames of a manifold M as an extension of the bundle e50cbc5a7a6f11fc165bd16facec" title="Click to view the MathML source">F2M of holonomic second order frames of M , we introduce in 16e6475c2e261b12e"> a principal bundle structure over e50cbc5a7a6f11fc165bd16facec" title="Click to view the MathML source">F2M, the structure group being the additive group A2(n) of skew-symmetric bilinear maps from Rn×Rn into Rn. The composition of the projection of that structure with the existing projection of the bundle of non-holonomic second order frames of M over 16e6475c2e261b12e"> provides a principal bundle structure in over e50cbc5a7a6f11fc165bd16facec" title="Click to view the MathML source">F2M. These results close an existing gap in the theory of second order frame bundles.