I'm using document class report and I have decided for chapter headings to use one of the predefined style of Vincent Zoonekynd's like this:

\documentclass{report}
\usepackage{xcolor}
\makeatletter
\def\LigneVerticale{\vrule height 1.5cm depth 0.9cm\hspace{0.1cm}\relax}
\def\LignesVerticales{%
\let\LV\LigneVerticale\LV\LV\LV\LV\LV\LV\LV\LV\LV\LV}
\def\GrosCarreAvecUnChiffre#1{{\setlength{\fboxsep}{-\fboxrule}%
\fbox{\color{white}%
\rlap{\vrule height 0.8cm width 1cm depth 0.2cm}%
\rlap{\hbox to 1cm{\hss\mbox{\color{black}#1}\hss}}%
\vrule height 0pt width 1cm depth 0pt}}}
\vspace*{-20pt}
\hbox{%
\huge\bfseries
\LignesVerticales
\hspace{-0.5cm}%
\GrosCarreAvecUnChiffre{\thechapter}
\hspace{0.2cm}\hbox{#1}%
}\par\vskip 0.5cm}
\vspace*{-20pt}
{\hbox{%
\huge\bfseries
\LignesVerticales
%\hspace{0.5cm}%
\hbox{#1}%
}\par\vskip 0.3cm}
\makeatother

\begin{document}
\chapter{Here we go}
\end{document}


However, I would like to make some changes.

1. I would need to move all construction up to the page, in other words to get smaller space between the top of any page and the construction.

2. I would like to change the small box. I would prefer white square with black number (not like this one-black square with white number).

-
I've taken the liberty of expanding your code into a compilable MWE (minimum working example), incorporating your note that you use the report document class. The main change is that I had to change the instruction \white #1 to \textcolor{white}{#1}. –  Mico May 18 '12 at 16:05

1. Since you've redefined \@makechapterhead and \@makeschapterhead (responsible for creating the entire chapter header when using \chapter and \chapter*, respectively), the chapter heading starts at the top of the text block. You may be referring to moving the entire text block up (or reduce the top margin). For this I would suggest using geometry.

2. Here's a MWE that provides what you're after. However, inserting a white block with a black number doesn't show up as needed:

\documentclass{report}
\usepackage{showframe}% http://ctan.org/pkg/showframe
\usepackage{xcolor}% http://ctan.org/pkg/xcolor

\makeatletter
\def\LigneVerticale{\vrule height 2cm depth 1.4cm\hspace{0.1cm}\relax}
\def\LignesVerticales{%
\let\LV\LigneVerticale\LV\LV\LV\LV\LV\LV\LV\LV\LV\LV}
\def\GrosCarreAvecUnChiffre#1{{%
\color{white}%
\rlap{\vrule height 0.8cm width 1cm depth 0.2cm}%
\rlap{\hbox to 1cm{\hss\mbox{\color{black}#1}\hss}}%
\vrule height 0pt width 1cm depth 0pt}}

\huge\bfseries
\LignesVerticales
\hspace{-0.5cm}%
\GrosCarreAvecUnChiffre{\thechapter}
\hspace{0.2cm}\hbox{#1}%
}\par\vskip 0.3cm}

\huge\bfseries
\LignesVerticales
%\hspace{0.5cm}%
\hbox{#1}%
}\par\vskip 0.3cm}
\makeatother

\begin{document}

\chapter{A chapter}

\end{document}


The following definition of \GrosCarreAveUnChiffre

\def\GrosCarreAvecUnChiffre#1{{\setlength{\fboxsep}{-\fboxrule}%
\fbox{\color{white}%
\rlap{\vrule height 0.8cm width 1cm depth 0.2cm}%
\rlap{\hbox to 1cm{\hss\mbox{\color{black}#1}\hss}}%
\vrule height 0pt width 1cm depth 0pt}}}


yields a boxes chapter number:

Another alternative - moving the header construction vertically is obtained using

\def\@makechapterhead#1{%
\hbox{%
\huge\bfseries
\LignesVerticales
\hspace{-0.5cm}%
\GrosCarreAvecUnChiffre{\thechapter}
\hspace{0.2cm}\hbox{#1}%
}\par\vskip 0.3cm}

\hbox{%
\huge\bfseries
\LignesVerticales
%\hspace{0.5cm}%
\hbox{#1}%
}\par\vskip 0.3cm}


which moves the vertical lines to the top of the page header. Of course, replacing the expression within \vspace* with a fixed dimension (say, -30pt) will displace it vertically with that amount.

showframe was added to highlight the text block boundary (in response to (1) above).

-
&Werner: Thank you. That's almost what I wanted. I just wanted to ask if you know how to put around the white square black borders. –  Laura May 18 '12 at 21:07
Don't use showframe package in the above. The rest of it is defined as above. Now I want to move all together (lines and chapter number and chapter name) up closer to the top of the page. I don't like too much empty space above the construction. –  Laura May 18 '12 at 22:33
@Jane: As mentioned in my answer, you don't need to showframe package. I just added it to provide a frame of reference. So, by all means, remove it. It should solve your problem of moving the header upward by inserting \vspace*{<len>} (where you specify <len>, a negative length) as I've indicated. –  Werner May 18 '12 at 22:40
@ Werner: Thank you for help. It works now. –  Laura May 19 '12 at 9:26