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The man behind Real Madrid's sporting policy said that the change was needed in order to halt a slide that has seen Real Madrid lose three of their last four games.
That run has seen Real Madrid slip down to fifth in the Primera Liga table, nine points behind league leaders Barcelona, who they must play in the Camp Nou stadium on Saturday night.
"We had a friendly meeting in which we explained all of the problems we have had in recent weeks," said Mijatovic in a press conference held at the Santiago Bernabeu Stadium.
"He (Schuster) accepted it well, although with sadness, because it is never easy to accept news like this. There are always negative and positive runs in football," he added.
Schuster spent most of the summer asking for Real Madrid to make new signings, but with the club wasting the close season in a fruitless effort to sign Cristiano Ronaldo, the only player to arrive was midfielder Rafael Van der Vaart.
The German especially asked for a new striker, but the club has only just signed Klaas-Jan Huntelaar, who won't be able to play until January.
Meanwhile Ruud Van Nistelrooy has already missed over a month with a knee injury. Gonzalo Higuain and Arjen Robben have also missed games with physical problems.
Despite all of this, Mijatovic insisted that neither he nor club President Ramon Calderon, who was booed by the supporters in the Santiago Bernabeu on Sunday night, were to blame.
"Regarding the reaction of people in the last game: our President has no blame for the current situation of the first team," said Mijatovic.
Meanwhile Ramos, who was sacked himself by Premier League side Tottenham Hotspurs earlier this season, promised to turn around the club's fortunes, starting in the Camp Nou.
"I hope to not disappoint anyone and achieve the success the club deserves. Barcelona is playing very well, but Real Madird has the prestige to not renounce the triumph in any ground in the World," he said.
"At the moment the most important thing is to strengthen the morale in the squad."
"I think that Real Madrid have the best defense in the world, there is enough to work with. It is not a problem of the defenders. When we attack it is collective work and it has to be the same when we defend," said the new Real Madrid coach.