Title: Examples of finite dimensional algebras which do not satisfy the derived Jordan--Hölder property,
Abstract: We construct a matrix algebra $\Lambda(A,B)$ from two given finite
dimensional elementary algebras $A$ and $B$ and give some sufficient conditions
on $A$ and $B$ under which the derived Jordan--Hölder property (DJHP) fails
for $\Lambda(A,B)$. This provides finite dimensional algebras of finite global
dimension which do not satisfy DJHP.