Cloud Computing introduces a novel computing paradigm that allows the users to run their applications on a customized environment using on-demand resources. This novel computing concept is enabled by several technologies including the Web, virtualization, distributed file systems as well as parallel programming models. For parallel computing on the Cloud, MapReduce is currently the first choice for Cloud providers to deliver data analysis services because this model is specially designed for data-intensive applications while a Cloud centre is actually also a data centre hosting a huge amount of data usually in Petascale. The current deployment of MapReduce on the Cloud, however, follows the traditional execution model of MapReduce that needs the support of a cluster manager. This means that the single virtual machines created on the Cloud have to be organized into a cluster in order to be capable of running a MapReduce application. This is not only a burden for system management but also prohibits inter-Cloud computing that can involve the resources of different Clouds to solve large problems with big data or distributed data. We developed a software framework for individual virtual machines to execute a MapReduce application in a parallel/collaborative way without the necessity of installing a middleware or specific software package for system management. A focus of this research work is a Single-Sign-On (SSON) mechanism that enables the remote access to the individual machines. We validated the SSON mechanism together with the entire MapReduce framework using a private Cloud. Experimental results show both the functionality and the feasibility of our approach.