  We present a general formalism to investigate the integrable properties of a
large class of non-ultralocal models which in principle allows the construction
of the corresponding lattice versions. Our main motivation comes from the
su(1|1) subsector of the string theory on AdS_5 x S^5 in the uniform gauge,
where such type of non-ultralocality appears in the resulting
Alday-Arutyunov-Frolov (AAF) model. We first show how to account for the second
derivative of the delta function in the Lax algebra of the AAF model by
modifying Maillet's r- and s-matrices formalism, and derive a well-defined
algebra of transition matrices, which allows for the lattice formulation of the
theory. We illustrate our formalism on the examples of the bosonic
Wadati-Konno-Ichikawa-Shimizu (WKIS) model and the two-dimensional free massive
Dirac fermion model, which can be obtained by a consistent reduction of the
full AAF model, and give the explicit forms of their corresponding r-matrices.
