New classes of linearly independent ternary transforms over Galois Field (3) called linearly independent helix transforms are introduced here. Four types of such helix transform matrices with detailed recursive equations are described. Various properties of helix transform matrices, their mutual relations and special cases for selected temary logic hnctions as well as their butterfly diagrams and computational costs are also discussed. Experimental results comparing four new helix transforms with ternary Reed-Muller transforms are also discussed.