A winding geometry for the construction of coreless transformers has been devised. The geometry can be employed for the construction of transformers with both a high turn ratio and high coupling factor. If made with superconductors, the transformers could find applications for matching the input coil of a SQUID to a high impedance source. A turn ratio of 1500 with a coupling factork=0.91 has been obtained experimentally using commercial wire. The high power superconducting version of this transformer could also find application at advanced energy distribution sites. ©1995 American Institute of Physics.