Sampling streams of continuous data with limited memory, or reservoir sampling, is a utility algorithm. Standard reservoir sampling maintains a random sample of the entire stream as it has arrived so far. This restriction does not meet the requirement of many applications that need to give preference to recent data. The simplest algorithm for maintaining a random sample of a sliding window reproduces periodically the same sample design. This is also undesirable for many applications. Other existing algorithms are using variable size memory, variable size samples or maintain biased samples and allow expired data in the sample. We propose an effective algorithm, which is very simple and therefore efficient, for maintaining a near random fixed size sample of a sliding window. Indeed our algorithm maintains a biased sample that may contain expired data. Yet it is a good approximation of a random sample with expired data being present with low probability. We analytically explain why and under which parameter settings the algorithm is effective. We empirically evaluate its performance (effectiveness) and compare it with the performance of existing representatives of random sampling over sliding windows and biased sampling algorithm.