  There is a cell decomposition of the nonnegative Grassmannian. For each cell,
totally positive bases(TP-bases) is defined as the minimal set of Pl\"ucker
variables such that all other nonzero Pl\"ucker variables in the cell can be
expressed in those variables in a subtraction-free rational function. This is
the generalization of the TP-bases defined for nonnegative part of $GL_k$
defined in \cite{FZ5}.
  For each cell, we have a $\LE$-diagram and a natural way to label the dots
inside the diagram with Pl\"ucker variables. Those set of Pl\"ucker variables
form a TP-bases of the cell. Using mutations coming from 3-term Pl\"ucker
relation, we conjecture that they can be mutated to a special set of Pl\"ucker
variable $\S$. All other nonzero Pl\"ucker variables in the cell will be
expressed as a subtraction-free Laurent polynomial in variables of $\S$. We
define TP-diagrams to express the transformation procedure in terms of moves on
a diagram.
  We will prove the conjecture for certain class of cells called
weakly-connected cells. Then we will study the connection with cluster algebras
through lattice-path-matroid cells.
