  A new $(1,1)$-dimensional super vector bundle which exists on any super
Riemann surface is described. Cross-sections of this bundle provide a new class
of fields on a super Riemann surface which closely resemble holomorphic
functions on a super Riemann surface, but which (in contrast to the case with
holomorphic functions) form spaces which have a well defined dimension which
does not change as odd moduli become non-zero.
