Suppress the header on first bookpart page

[Helge Kruse]

I want to write all instrument's part in one book. I use a bookpart for 
each instrument. The headline should identify the piece, instrument and 
page to reduce the time for sort pages when all sheets dropped to the 
floor. ;-)

For each instrument I have a header. How I can I suppress the head line 
for the pages with header. That's the first page of a bookpart?

Regards
Helge

Example:

\version "2.16.0"

\paper {
  oddHeaderMarkup = \markup \fill-line {
    \on-the-fly #not-first-page \fromproperty #'header:composer
    \on-the-fly #not-first-page \fromproperty #'header:title
    \on-the-fly #not-first-page \fromproperty #'header:instrument
    \on-the-fly #print-page-number-check-first \fromproperty 
#'page:page-number-string
  }
  evenHeaderMarkup = \markup \fill-line {
    \on-the-fly #not-first-page \fromproperty #'header:composer
    \on-the-fly #not-first-page \fromproperty #'header:title
    \on-the-fly #not-first-page \fromproperty #'header:instrument
    \on-the-fly #print-page-number-check-first \fromproperty 
#'page:page-number-string
  }
}

\header {
  title = "Melancholia"
  composer = "The one who must not be named"
}

music = \relative c' { \repeat unfold 200 { c2 r4 r } }

\book {
  \bookpart {
    \header { instrument = "Violino 1" }
    \score { \music }
  }
  \bookpart {
    \header { instrument = "Violino 2" }
    \score { \music }
  }
}