Flowchart drawing (Complicated Arrows)

One way to draw the outer lines would be to define intermediate coordinates:

\coordinate (Above m1) at ($(m1.north)+(0,1.0cm)$); \coordinate (Below r5l) at ($(r5l.south) + (0,-1.0cm)$); \draw[ultra thick, blue, ->] (r5l.south) -- (Below r5l) -- ++ (7.5cm,0) |- (Above m1) -- (m1.north) ; 

And for the "zig-zag":

\draw [ultra thick, orange, ->] (m4.west) -- ++(-2.0cm,0) |- (l3.east) ; \draw [ultra thick, orange, ->] (m6.west) -- ++(-2.0cm,0); 

Using similar techniques you should be able to draw the rest of the arrows.

Notes:

• The ++(x,y) syntax means the coordinate located at the current position with a translation of (x,y) applied. So ++(-2.0cm,0) means the point 2.0cm to the left.
• A \coordinate defines a name for a specific point. So, \coordinate (Above m1) at ($(m1.north)+(0,1.0cm)$) defines a coordinate named (Above m1) which corresponds to the vector addition of (m1.north) and (0,1.0cm). So 1.0cm above the north point of m1.

Code:

\documentclass[a4paper]{article} \usepackage[top=1cm,bottom=1cm,left=1cm,landscape]{geometry} \usepackage{tikz} \usetikzlibrary{calc} %\usetikzlibrary{arrows,arrows.meta} %\input{arrowsnew} \begin{document} \tikzstyle{mbigblock} = [rectangle, draw, text width=13cm, text centered, rounded corners, minimum height=1em] \tikzstyle{block} = [rectangle, draw, text width=3.5cm, text centered, minimum height=1em] \tikzstyle{lblock} = [rectangle, draw, text width=5cm, text centered, minimum height=1em] \tikzstyle{rblock} = [rectangle, draw, text width=3.5cm, text centered, minimum height=1em] \begin{tikzpicture}[node distance=2cm,scale=0.8] % middle boxes \node (m1) [mbigblock] {Choose an exhaustive summary, $\kappa$, with $p$ parameters $\theta$}; \node (m2) [mbigblock,below of=m1,node distance=1cm] {Find the rank, $r$, of the derivative matrix $D=\partial \kappa / \partial \theta$}; \node (m3) [block,below of=m2] {Model is full rank and at least locally identifiable (Th2 a. i.)}; \node (m4) [block,below of=m3] {Does the model extend?}; \node (m5) [block,below of=m4] {Can the extension theorem be used?}; \node (m6) [block,below of=m5] {If $D_{ex}$ is full rank, the model is full rank in general (Th3)}; \node (m7) [block,below of=m6,text width=2cm] {Is $r_s \geq p$?}; \node (m8l) [block,below left of=m7,node distance=2.5cm,text width=3cm] {Model is full rank and at least locally identifiable (Th 8b).}; \node (m8r) [block,below right of=m7,node distance=2.5cm,text width=3cm] {Model is parameter redundant and non--identifiable (Th 8b).}; \node (m9) [block,below of=m7,node distance=3.5cm,text width=2cm] {Is $r_s = p$?}; \node (m10l) [block,below left of=m9,node distance=2.5cm,text width=3cm] {Solve PDE to find a reduced--form exhaustive summary}; \node (m10r) [block,below right of=m9,node distance=2.5cm,text width=3cm] {$s$ is a reduced--form exhaustive summary}; % left boxes \node (l1) [lblock,left of=m3,node distance=8cm] {Model is parameter redundant and not identifiable. There are $r$ estimable parameters. (Th2a.ii)}; \node (l2) [lblock,below of=l1,node distance=3cm] {Solve $\alpha^T D=0$ and PDE(9) to find the set of estimable parameters, $\beta$(Th2b). Let $\theta=\beta$ and find the new $D$. What follows applies to the new set of parameters, from this results for the original $\theta$ can be deduced.}; \node (l3) [lblock,below of=l2,node distance=5cm] {Write $D=PLUR$. Does Det$(U)=0$ have any solutions (for which $R$ is defined)(Th4)? If appropriate write $D_{ex}=P_{ex}L_{ex}U_{ex}R_{ex}$. Does Det$(U_{ex})=0$ have any solutions (Th6)}; \node (l4l) [block,below left of=l3,node distance=4cm,text width=6em] {Conditionally Full Rank}; \node (l4r) [block,below right of=l3,node distance=4cm,text width=6em] {Essentially Full Rank}; \node (l5l) [block,below of=l4l,text width=6em] {Determine parameter redundant submodels if appropriate.}; \node (l5r) [block,below of=l4r,text width=6em,minimum height=6em] {Test for global identifiability}; % right boxes \node (r1) [block,right of=m3,node distance=8cm] {Choose a reparameterisation $s$ of length $p_s$}; \node (r2) [block,below of=r1,node distance=4cm] {Rewrite $\kappa$ in terms of $s$. Find the rank $r_s$, of the derivative matrix $D_s=\partial \kappa(s)/\partial s$}; \node (r3) [block,below of=r2,node distance=3cm] {Is rank$(\partial s / \partial \theta)=p_s$ ?}; \node (r4) [block,right of=m9,node distance=8cm,text width=2cm] {Is $r_s=p_s$}; \node (r5l) [block,below left of=r4,node distance=2.5cm,text width=3cm] {Solve PDE to find an exhaustive summary}; \node (r5r) [block,below right of=r4,node distance=2.5cm,text width=3cm] {$s$ is an exhaustive summary (remark 6)}; \draw[ultra thick, red ] (r5r.south) -- ++ (0,-1.0cm); % Middle flows \draw[->] (m1) -- (m2) ; \draw[->] (m2) -- node[left] {$r=p$} (m3) ; \draw[->] (m3) -- (m4) ; \draw[->] (m4) -- node[left] {Yes} (m5) ; \draw[->] (m5) -- node[left] {Yes} (m6) ; \draw[->] (m7) -| node[left] {Yes} (m8l); \draw[->] (m7) -| node[right] {No } (m8r); \draw[->] (m9) -| node[left] {No} (m10l); \draw[->] (m9) -| node[right] {Yes} (m10r); % Right flows \draw[->] (r1) -- (r2) ; \draw[->] (r2) -- (r3) ; \draw[->] (r3) -- (r4) ; \draw[->] (r4) -| node[left] {No} (r5l); \draw[->] (r4) -| node[right] {Yes} (r5r); % Left flows \draw[->] (l1) -- (l2) ; %\draw[->] (l3) |-| node[left] {Yes} (l4l); %\draw[->] (l3) |-| node[right] {No } (l4r); \draw[->] (l4l) -- (l5l) ; \draw[->] (l4r) -- (l5r) ; % Middle to left % \draw[->] (m4.west) -| (l3.east) ; % Middle to right % Right to middle \draw[->] (r3.west) -| (m7.north) ; %% Draw the outer lines \coordinate (Above m1) at ($(m1.north)+(0,1.0cm)$); \coordinate (Below r5l) at ($(r5l.south) + (0,-1.0cm)$); \draw[ultra thick, blue, ->] (r5l.south) -- (Below r5l) -- ++ (7.5cm,0) |- (Above m1) -- (m1.north) ; \draw [ultra thick, orange, ->] (m4.west) -- ++(-2.0cm,0) |- (l3.east) ; \draw [ultra thick, orange, ->] (m6.west) -- ++(-2.0cm,0); \end{tikzpicture} \end{document}