The decomposition of vegetable matter into compost is said to be exotherimic in nature...but all decomposition reactions involve the absortion of enegry ; i.e. they are endothermic.

Can a particular reaction be both exothermic and endothermic ???

Decomposition reaction may not always require energy, but usually they require energy and is called endothermic reaction.  whether the process is exothermic or endothermic depends upon the overall enthalpy of reaction. sometimes to decompose a substance, the reaction may need energy, but the energy released of the products can be so large that the overall process can be termed as exothermic. The decomposition of plant and animal organic waste by the action of microbes into useful compost is an exothermic reaction because large amount of energy is released in this process. It is different from other chemical reactions,as they need energy to break the bond. But in these reaction the breakdown is carried out by microbes.