We propose and implement a nondestructive measurement that distinguishes between two-electron spin states in a quantum dot. In contrast to earlier experiments with quantum dots, the spins are left behind in the state corresponding to the measurement outcome. By measuring the spin states twice within a time shorter than the relaxation time T(1), correlations between the outcomes of consecutive measurements are observed. They disappear as the wait time between measurements becomes comparable to T(1). The correlation between the postmeasurement state and the measurement outcome is measured to be similar to 90% on average.